Uploaded by Evan Miceli

PS160 Equation Sheet

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PS160 Equation Sheet
Useful Constants
L · atm
mol · K
c = 2.99792458 ⇥ 108 m/s
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8
<latexit sha1_base64="80BDBS9y3l5jntticuP5OwJKdao=">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</latexit>
= 5.67 ⇥ 10
<latexit sha1_base64="5/EyLihTZM9mFcIe7UqDPGvk4Vc=">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</latexit>
2
W/(m · K )
k = R/NA = 1.381 ⇥ 10
m
⇢=
V
<latexit sha1_base64="uwIPqdyVz/vWSRGVx2w93EPJ37o=">AAACGHicbVDLSgNBEJz1GeMr6tHLYBACgbgbRL0IAS8eI5gHZGOYncwmg7Mzy0yvEJb9DC/+ihcPinjNzb9x8jhoYkFDUdVNd1cQC27Adb+dldW19Y3N3FZ+e2d3b79wcNg0KtGUNagSSrcDYpjgkjWAg2DtWDMSBYK1gsebid96YtpwJe9hFLNuRAaSh5wSsFKvcBaXfT1UeDAq+6EmNPWytJpNpaeH6rUfERjqKKVKGiASsl6h6FbcKfAy8eakiOao9wpjv69oEjEJVBBjOp4bQzclGjgVLMv7iWExoY9kwDqWShIx002nj2X41Cp9HCptSwKeqr8nUhIZM4oC2zk51Cx6E/E/r5NAeNVNuYwTYJLOFoWJwKDwJCXc55pRECNLCNXc3orpkNh8wGaZtyF4iy8vk2a14l1Uzu/Oi7XSPI4cOkYnqIQ8dIlq6BbVUQNR9Ixe0Tv6cF6cN+fT+Zq1rjjzmSP0B874By8ZoHU=</latexit>
<latexit sha1_base64="11tNJD8Cxw87El8m/thY0fhS3ZI=">AAAB+3icbVDLSsNAFJ3UV62vWJduBovQVUmkqBuh4MZlBfuAJpTJdNIOnUeYmYgl5FfcuFDErT/izr9x2mahrQcuHM65l3vviRJGtfG8b6e0sbm1vVPereztHxweucfVrpapwqSDJZOqHyFNGBWkY6hhpJ8ognjESC+a3s793iNRmkrxYGYJCTkaCxpTjIyVhm41UBMJb2AQK4QznmfdfOjWvIa3AFwnfkFqoEB76H4FI4lTToTBDGk98L3EhBlShmJG8kqQapIgPEVjMrBUIE50mC1uz+G5VUYwlsqWMHCh/p7IENd6xiPbyZGZ6FVvLv7nDVITX4cZFUlqiMDLRXHKoJFwHgQcUUWwYTNLEFbU3grxBNkUjI2rYkPwV19eJ92Lhn/ZaN43a616EUcZnIIzUAc+uAItcAfaoAMweALP4BW8Obnz4rw7H8vWklPMnIA/cD5/AJ0JlBs=</latexit>
4
23
R = 8.3145 J/(mol · K) = 0.08206
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J/K
1
p + ⇢gy + ⇢v 2 = constant
2
1
T
<latexit sha1_base64="4jBYoQOqcHujC14JLpxo1o/5c1g=">AAAB+nicbVDLSsNAFJ3UV62vVJduBovQjSWRom6EghuXFewD2hAm00k7dGYSZibaEvMpblwo4tYvceffOG2z0NYDFw7n3Mu99wQxo0o7zrdVWFvf2Nwqbpd2dvf2D+zyYVtFicSkhSMWyW6AFGFUkJammpFuLAniASOdYHwz8zsPRCoaiXs9jYnH0VDQkGKkjeTbZeRPrs/6oUQ4HWcpzya+XXFqzhxwlbg5qYAcTd/+6g8inHAiNGZIqZ7rxNpLkdQUM5KV+okiMcJjNCQ9QwXiRHnp/PQMnhplAMNImhIaztXfEyniSk15YDo50iO17M3E/7xeosMrL6UiTjQReLEoTBjUEZzlAAdUEqzZ1BCEJTW3QjxCJgZt0iqZENzll1dJ+7zmXtTqd/VKo5rHUQTH4ARUgQsuQQPcgiZoAQwewTN4BW/Wk/VivVsfi9aClc8cgT+wPn8AiI2UHg==</latexit>
<latexit sha1_base64="d2b61c70o0R99lkmQCXjAZXHYbM=">AAAConicbZFNa9wwEIa17lfqfiRpj72IbgM5lMUOoc0lEOil9FCSNpsE1iZI8nhXRB+uNM5mMaY/o9f2Z/XfVN74kN10QPDwzjuakYZXSnpMkr+D6MHDR4+fbDyNnz1/8XJza/vVmbe1EzAWVll3wZkHJQ2MUaKCi8oB01zBOb/61OXPr8F5ac0pLirINZsaWUrBMEh5ZjVM2eFeVklaXm4Nk1GyDHof0h6GpI/jy+3Bz6ywotZgUCjm/SRNKswb5lAKBW2c1R4qJq7YFCYBDdPg82Y5dUt3glLQ0rpwDNKlereiYdr7hebBqRnO/HquE/+Xm9RYHuSNNFWNYMRto7JWFC3tvoAW0oFAtQjAhJNhVipmzDGB4aNWunDdxjt3BQNzvEG4wfdL6keYAnoqlPXQ9TiV4ZX0K8zpN6uZofMZGGoACijiOAt1wuqgF03G3TWIdpLmTRagybqLedkM07Zt15yrRq57U1hZur6g+3C2N0o/jPZP9odHu/3yNsgb8pbskpR8JEfkMzkmYyLID/KL/CZ/onfRl+gk+n5rjQZ9zWuyElH2D/oV0aI=</latexit>
ax =
! = 2⇡f
k
x
m
=
=
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<latexit sha1_base64="B9DqL3nXXZNS5jIKwA9TVr8bGwY=">AAAB8nicbVBNSwMxFMzWr1q/qh69BIvQU9mVol6EghePFWwtbJeSzWbb0GyyJG8LZenP8OJBEa/+Gm/+G9N2D9o6EBhm5pH3JkwFN+C6305pY3Nre6e8W9nbPzg8qh6fdI3KNGUdqoTSvZAYJrhkHeAgWC/VjCShYE/h+G7uP02YNlzJR5imLEjIUPKYUwJW8ie3fWHDEcHxoFpzG+4CeJ14BamhAu1B9asfKZolTAIVxBjfc1MIcqKBU8FmlX5mWEromAyZb6kkCTNBvlh5hi+sEuFYafsk4IX6eyIniTHTJLTJhMDIrHpz8T/PzyC+CXIu0wyYpMuP4kxgUHh+P464ZhTE1BJCNbe7YjoimlCwLVVsCd7qyeuke9nwrhrNh2atVS/qKKMzdI7qyEPXqIXuURt1EEUKPaNX9OaA8+K8Ox/LaMkpZk7RHzifP7KKkM0=</latexit>
v= f
v=
p
<latexit sha1_base64="2pTFTdn/V6H9yslaxJA01YDo4hw=">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</latexit>
p
<latexit sha1_base64="Y/T8cRJgOPGbAWWw9vee9whiaUI=">AAACInicbVDLSgMxFM3UV62vqks3waJ01c5I8bEQim7cCFX6UDpDyaSZNjSZGZNMoQz9Fjf+ihsXiroS/BjTdoTaeiBwOOdcbu5xQ0alMs0vI7WwuLS8kl7NrK1vbG5lt3fqMogEJjUcsEDcuUgSRn1SU1QxchcKgrjLSMPtXY78Rp8ISQO/qgYhcTjq+NSjGCkttbJn/cNzWz4IFV8UbdENhrad+VXsDuIcwdtq8Xpavp8EW9mcWTDHgPPESkgOJKi0sh92O8ARJ77CDEnZtMxQOTESimJGhhk7kiREuIc6pKmpjziRTjw+cQgPtNKGXiD08xUcq9MTMeJSDrirkxyprpz1RuJ/XjNS3qkTUz+MFPHxZJEXMagCOOoLtqkgWLGBJggLqv8KcRcJhJVuNaNLsGZPnif1o4J1XCjdlHLlfFJHGuyBfZAHFjgBZXAFKqAGMHgEz+AVvBlPxovxbnxOoikjmdkFf2B8/wDi/qM1</latexit>
v=
p
=
p
=
Pav
F/µ
TF =
9
TC + 32
5
RT /M
Y /⇢
<latexit sha1_base64="ZhTl99SsqeoVPZP1nAvMHA7y8V0=">AAACCXicbVDLSsNAFJ34rPUVdelmsAgFISS1WjdCoRvBTYW+oA1hMp20QycPZiZCCdm68VfcuFDErX/gzr9x0gbU1gMDZ865l3vvcSNGhTTNL21ldW19Y7OwVdze2d3b1w8OOyKMOSZtHLKQ91wkCKMBaUsqGelFnCDfZaTrThqZ370nXNAwaMlpRGwfjQLqUYykkhwdtpyBj+SY+8ltev3zaaRnldq5YV04esk0zBngMrFyUgI5mo7+ORiGOPZJIDFDQvQtM5J2grikmJG0OIgFiRCeoBHpKxognwg7mV2SwlOlDKEXcvUCCWfq744E+UJMfVdVZouKRS8T//P6sfSu7IQGUSxJgOeDvJhBGcIsFjiknGDJpoogzKnaFeIx4ghLFV5RhWAtnrxMOhXDujSqd9VSvZzHUQDH4ASUgQVqoA5uQBO0AQYP4Am8gFftUXvW3rT3eemKlvccgT/QPr4B9pGZIA==</latexit>
p
g/L
mgd/I
<latexit sha1_base64="N+Jc/XHO32BEvCQzm66JKbBpH2E=">AAACDHicbVDLSgMxFL3js9ZX1aWbYBG6KjNDUTdCwY3uKtgHtOOQSTNtaCYzJBmhDPMBbvwVNy4UcesHuPNvTB8Lbb2Q3JNz7uXmniDhTGnb/rZWVtfWNzYLW8Xtnd29/dLBYUvFqSS0SWIey06AFeVM0KZmmtNOIimOAk7bwehqorcfqFQsFnd6nFAvwgPBQkawNpRfKvdCiUl24zu5udz8cvaWvnvv5iY5Jpkqu2pPAy0DZw7KMI+GX/rq9WOSRlRowrFSXcdOtJdhqRnhNC/2UkUTTEZ4QLsGChxR5WXTZXJ0apg+CmNpjtBoyv7uyHCk1DgKTGWE9VAtahPyP62b6vDCy5hIUk0FmQ0KU450jCbOoD6TlGg+NgATycxfERli44Y2/hWNCc7iysug5Vads2rttlauV+Z2FOAYTqACDpxDHa6hAU0g8AjP8Apv1pP1Yr1bH7PSFWvecwR/wvr8AfsAmt0=</latexit>
<latexit sha1_base64="iHQkPgd8DION52qkxs04j3YjY3I=">AAACAnicbVDLSsNAFJ3UV62vqCtxM1iEbiyJFHUjFNy4rGAf0IYwmU7aoTOTMDMRSghu/BU3LhRx61e482+ctFlo64ELh3Pu5d57gphRpR3n2yqtrK6tb5Q3K1vbO7t79v5BR0WJxKSNIxbJXoAUYVSQtqaakV4sCeIBI91gcpP73QciFY3EvZ7GxONoJGhIMdJG8u2j0E8HHOmx5GlAkM6y69BHZ6Ef+HbVqTszwGXiFqQKCrR8+2swjHDCidCYIaX6rhNrL0VSU8xIVhkkisQIT9CI9A0ViBPlpbMXMnhqlCEMI2lKaDhTf0+kiCs15YHpzK9Vi14u/uf1Ex1eeSkVcaKJwPNFYcKgjmCeBxxSSbBmU0MQltTcCvEYSYS1Sa1iQnAXX14mnfO6e1Fv3DWqzVoRRxkcgxNQAy64BE1wC1qgDTB4BM/gFbxZT9aL9W59zFtLVjFzCP7A+vwBo0qXgQ==</latexit>
I1
r2
= 22
I2
r1
TK = TC + 273.15
fbeat = fa
<latexit sha1_base64="x9TlyaFPIEvT09myFDRlkLEjqak=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSL0VJJS1IvQ4sVjBfsBbQib7aZdutnE3U2ghP4OLx4U8eqP8ea/cdvmoK0PBh7vzTAzz485U9q2v62Nza3tnd3CXnH/4PDouHRy2lFRIgltk4hHsudjRTkTtK2Z5rQXS4pDn9OuP7mb+92USsUi8ainMXVDPBIsYARrI7lNz0k957bp1VKv5pXKdtVeAK0TJydlyNHySl+DYUSSkApNOFaq79ixdjMsNSOczoqDRNEYkwke0b6hAodUudni6Bm6NMoQBZE0JTRaqL8nMhwqNQ190xliPVar3lz8z+snOrhxMybiRFNBlouChCMdoXkCaMgkJZpPDcFEMnMrImMsMdEmp6IJwVl9eZ10alXnqlp/qJcblTyOApzDBVTAgWtowD20oA0EnuAZXuHNSq0X6936WLZuWPnMGfyB9fkD8daQ2A==</latexit>
A1 v 1 = A2 v 2
1
1
mv 2 + kx2
2
2
1 2
= kA = constant
2
E=
<latexit sha1_base64="5x289jKXyH3AT4BPFMssxRZezSU=">AAAB/3icbVBNS8NAEJ34WetXVPDiJViEnkpSinopFLx48FDBfkAbwma7aZduNmF3UygxB/+KFw+KePVvePPfuG1z0NYHA4/3ZpiZ58eMSmXb38ba+sbm1nZhp7i7t39waB4dt2WUCExaOGKR6PpIEkY5aSmqGOnGgqDQZ6Tjj29mfmdChKQRf1DTmLghGnIaUIyUljzzNPB4nfcDgXA6ydLqXVbnged4Zsmu2HNYq8TJSQlyND3zqz+IcBISrjBDUvYcO1ZuioSimJGs2E8kiREeoyHpacpRSKSbzu/PrAutDKwgErq4subq74kUhVJOQ193hkiN5LI3E//zeokKrt2U8jhRhOPFoiBhloqsWRjWgAqCFZtqgrCg+lYLj5DOQunIijoEZ/nlVdKuVpzLSu2+VmqU8zgKcAbnUAYHrqABt9CEFmB4hGd4hTfjyXgx3o2PReuakc+cwB8Ynz+xbJXR</latexit>
fn = n
I=
<latexit sha1_base64="LctfXgR0h8VTeZcnOiz1tqjghIE=">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</latexit>
<latexit sha1_base64="08+DSXhfvt9MnG4+/yjqWsD9scg=">AAACFnicbVDLSsNAFJ34rPUVdekmWISCWJJaXwuhUBCXFfqCJobJdNIOnUzCzEQoIV/hxl9x40IRt+LOv3HSFtTWAxcO59zLvfd4ESVCmuaXtrC4tLyymlvLr29sbm3rO7stEcYc4SYKacg7HhSYEoabkkiKOxHHMPAobnvDWua37zEXJGQNOYqwE8A+Iz5BUCrJ1Y8brh1AOeBBcp1e2T6HKLlMk9P0R6+lRyflOxsRjly9YJbMMYx5Yk1JAUxRd/VPuxeiOMBMIgqF6FpmJJ0EckkQxWnejgWOIBrCPu4qymCAhZOM30qNQ6X0DD/kqpg0xurviQQGQowCT3Vmp4pZLxP/87qx9C+chLAolpihySI/poYMjSwjo0c4RpKOFIGIE3WrgQZQRSNVknkVgjX78jxplUvWWalyWylUi9M4cmAfHIAisMA5qIIbUAdNgMADeAIv4FV71J61N+190rqgTWf2wB9oH9+Gtp+D</latexit>
p
<latexit sha1_base64="WOpM+GIsKG8wMw8RF3pbhFK5i3g=">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</latexit>
k/m
1p
⇢B! 2 A2
2
p
= p2max /2 ⇢B
<latexit sha1_base64="GKohg9eUfEnlpnbBkz40AWq5M3E=">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</latexit>
nv
fn =
(n = 1, 2, 3, ...)
2L
or
nv
fn =
(n = 1, 3, 5, ...)
4L
(depending on the pipe)
<latexit sha1_base64="75CNtXsKbAXhR64TDzae4n1J2Cg=">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</latexit>
p
1p
=
µF ! 2 A2
2
B/⇢
dV
= Av
dt
p = p0 + ⇢gh
!=
f=
<latexit sha1_base64="T9SfJtzKse5wxLW3dyFKvvEprug=">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</latexit>
<latexit sha1_base64="1SfJot6ifJ94JAcneVkntBokBy0=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBahp5JIUS9CxYvHCvYD2lA2m027dLMJu5NCCfknXjwo4tV/4s1/47bNQVsfDDzem2Fmnp8IrsFxvq3SxubW9k55t7K3f3B4ZB+fdHScKsraNBax6vlEM8ElawMHwXqJYiTyBev6k/u5350ypXksn2CWMC8iI8lDTgkYaWjbg1ARmgWdPAsgv72bDu2qU3cWwOvELUgVFWgN7a9BENM0YhKoIFr3XScBLyMKOBUsrwxSzRJCJ2TE+oZKEjHtZYvLc3xhlACHsTIlAS/U3xMZibSeRb7pjAiM9ao3F//z+imEN17GZZICk3S5KEwFhhjPY8ABV4yCmBlCqOLmVkzHxEQBJqyKCcFdfXmddC7r7lW98dioNmtFHGV0hs5RDbnoGjXRA2qhNqJoip7RK3qzMuvFerc+lq0lq5g5RX9gff4AvbeTqA==</latexit>
<latexit sha1_base64="HX6lCuaw//JdEuWg4zcnY7Wckd8=">AAAB9XicbVBNSwMxEJ31s9avqkcvwSIUhLIrRb0IBS8eK9gPaNeSTbPd0GyyJFmlLP0fXjwo4tX/4s1/Y9ruQVsfDDzem2FmXpBwpo3rfjsrq2vrG5uFreL2zu7efungsKVlqghtEsml6gRYU84EbRpmOO0kiuI44LQdjG6mfvuRKs2kuDfjhPoxHgoWMoKNlR6S66TvnvVUJNEQRf1S2a26M6Bl4uWkDDka/dJXbyBJGlNhCMdadz03MX6GlWGE00mxl2qaYDLCQ9q1VOCYaj+bXT1Bp1YZoFAqW8Kgmfp7IsOx1uM4sJ0xNpFe9Kbif143NeGVnzGRpIYKMl8UphwZiaYRoAFTlBg+tgQTxeytiERYYWJsUEUbgrf48jJpnVe9i2rtrlauV/I4CnAMJ1ABDy6hDrfQgCYQUPAMr/DmPDkvzrvzMW9dcfKZI/gD5/MHDTSRgA==</latexit>
<latexit sha1_base64="7xM/MmPLzMWisvtlMMt9aPeYemA=">AAACHXicbVDLSsNAFJ34rPEVdelmsFi6ahMp6qZQcKPgooJ9QBPKZDpNh84kcWYilNAfceOvuHGhiAs34t84bbOorQcGzj3nXu7c48eMSmXbP8bK6tr6xmZuy9ze2d3btw4OmzJKBCYNHLFItH0kCaMhaSiqGGnHgiDuM9Lyh1cTv/VIhKRReK9GMfE4CkLapxgpLXWtihtxEiBYqEJXPgiVDst87LpmoTorg/LtfMmDXvlm3LXydsmeAi4TJyN5kKHetb7cXoQTTkKFGZKy49ix8lIkFMWMjE03kSRGeIgC0tE0RJxIL51eN4anWunBfiT0CxWcqvMTKeJSjrivOzlSA7noTcT/vE6i+pdeSsM4USTEs0X9hEEVwUlUsEcFwYqNNEFYUP1XiAdIIKx0oKYOwVk8eZk0z0rOealyV8nXilkcOXAMTkAROOAC1MA1qIMGwOAJvIA38G48G6/Gh/E5a10xspkj8AfG9y+JZKDn</latexit>
<latexit sha1_base64="TAf/L/brbtPmFh4w1NiLRLFuum8=">AAAB9HicbVBNSwMxEJ3Ur1q/qh69BIvQU9mVol6EghePFfohtEvJptk2NJtdk2yhLPs7vHhQxKs/xpv/xrTdg7Y+GHi8N8PMPD8WXBvH+UaFjc2t7Z3ibmlv/+DwqHx80tFRoihr00hE6tEnmgkuWdtwI9hjrBgJfcG6/uRu7nenTGkeyZaZxcwLyUjygFNirOQFt/1AEZq6WdrKBuWKU3MWwOvEzUkFcjQH5a/+MKJJyKShgmjdc53YeClRhlPBslI/0SwmdEJGrGepJCHTXro4OsMXVhniIFK2pMEL9fdESkKtZ6FvO0NixnrVm4v/eb3EBDdeymWcGCbpclGQCGwiPE8AD7li1IiZJYQqbm/FdExsCsbmVLIhuKsvr5POZc29qtUf6pVGNY+jCGdwDlVw4RoacA9NaAOFJ3iGV3hDU/SC3tHHsrWA8plT+AP0+QOwepH7</latexit>
1
NA = 6.022 ⇥ 1023 mol
<latexit sha1_base64="azutoYK4IguuU2tmwMHM0ohskbo=">AAACEXicbVDLSsNAFJ34rPUVdelmsAhxUxIpKohQdGN3FewDmhAmk0k7dPJgZiKUkF9w46+4caGIW3fu/BsnbRbaeuDC4Zx7ufceL2FUSNP81paWV1bX1isb1c2t7Z1dfW+/K+KUY9LBMYt530OCMBqRjqSSkX7CCQo9Rnre+Kbwew+ECxpH93KSECdEw4gGFCOpJFc3bI9IdGVYpn1ph0iOeJj51/mJzeKhHXCEs1aetVwzd/WaWTengIvEKkkNlGi7+pftxzgNSSQxQ0IMLDORToa4pJiRvGqngiQIj9GQDBSNUEiEk00/yuGxUnwYxFxVJOFU/T2RoVCISeipzuJoMe8V4n/eIJXBhZPRKEklifBsUZAyKGNYxAN9ygmWbKIIwpyqWyEeIZWDVCFWVQjW/MuLpHtat87qjbtGrWmUcVTAITgCBrDAOWiCW9AGHYDBI3gGr+BNe9JetHftY9a6pJUzB+APtM8flxmc0g==</latexit>
= (10 dB) log
I
I0
v + vL
fS
v + vS
or
v ± vL
fL =
fS
v ⌥ vS
(depending on coordinate system)
<latexit sha1_base64="2GupXTe/zELv0BEetL07OyGbUqY=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAgFoSRS1I1ScOPCRUX7gCaUyXTSDp1JwsykUEL+xo2/4kZQEV36J07aLPrwwMC559zL3Hu8iFGpLOvHWFldW9/YLGwVt3d29/bNg8OmDGOBSQOHLBRtD0nCaEAaiipG2pEgiHuMtLzhbea3RkRIGgZPahwRl6N+QH2KkdJS17zxuw5HaiB4cp9eO75AOBmdjWbEdK5+TFN/puiaJatiTQCXiZ2TEshR75rvTi/EMSeBwgxJ2bGtSLkJEopiRtKiE0sSITxEfdLRNECcSDeZ3JnCU630oB8K/QIFJ+rsRIK4lGPu6c5sQ7noZeJ/XidW/pWb0CCKFQnw9CM/ZlCFMAsN9qggWLGxJggLqneFeIB0VkpHW9Qh2IsnL5PmecW+qFQfqqVaOY+jAI7BCSgDG1yCGrgDddAAGDyDV/ABPo0X4834Mr6nrStGPnME5mD8/gHWqqhT</latexit>
fL =
fb
<latexit sha1_base64="6DNqQpAKTB2L87Z536KyuhNvijY=">AAACB3icbZC7SgNBFIZn4y3G26qlIINBSBV2JaiNENDCwiJCbpBdltnJ2WTI7IWZWSEs6Wx8FRsLRWx9BTvfxkmyhSb+MPDxn3M4c34/4Uwqy/o2Ciura+sbxc3S1vbO7p65f9CWcSootGjMY9H1iQTOImgppjh0EwEk9Dl0/NH1tN55ACFZHDXVOAE3JIOIBYwSpS3PPHZugCuC7/AVdghPhho9C+du0zPLVtWaCS+DnUMZ5Wp45pfTj2kaQqQoJ1L2bCtRbkaEYpTDpOSkEhJCR2QAPY0RCUG62eyOCT7VTh8HsdAvUnjm/p7ISCjlOPR1Z0jUUC7WpuZ/tV6qgks3Y1GSKojofFGQcqxiPA0F95kAqvhYA6GC6b9iOiSCUKWjK+kQ7MWTl6F9VrXPq7X7WrleyeMooiN0girIRheojm5RA7UQRY/oGb2iN+PJeDHejY95a8HIZw7RHxmfP57Glyw=</latexit>
v
= nf1
2L
<latexit sha1_base64="jZPPwfE3/Z48LkWkh1fa2ur/wIg=">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</latexit>
<latexit sha1_base64="/JszDVYDnxXOdDxscYC21BBMxLI=">AAACBnicbZDLSsNAFIYnXmu9RV2KMFiErkoiRd0IBV24rNAbNCFMpift0MmFmYlQQldufBU3LhRx6zO4822ctFlo6w8DH/85hzPn9xPOpLKsb2NldW19Y7O0Vd7e2d3bNw8OOzJOBYU2jXksej6RwFkEbcUUh14igIQ+h64/vsnr3QcQksVRS00ScEMyjFjAKFHa8swT5xa4IriDr7HjQ06ehQuz5ZkVq2bNhJfBLqCCCjU988sZxDQNIVKUEyn7tpUoNyNCMcphWnZSCQmhYzKEvsaIhCDdbHbGFJ9pZ4CDWOgXKTxzf09kJJRyEvq6MyRqJBdruflfrZ+q4MrNWJSkCiI6XxSkHKsY55ngARNAFZ9oIFQw/VdMR0QQqnRyZR2CvXjyMnTOa/ZFrX5frzSqRRwldIxOURXZ6BI10B1qojai6BE9o1f0ZjwZL8a78TFvXTGKmSP0R8bnD+3Llsw=</latexit>
<latexit sha1_base64="61xdRgCXYsKZHycCYaWVN2Tl7qs=">AAAB83icbVBNSwMxEM3Wr1q/qh69BIvQU9mVol6Egh48ttDWQncp2XS2DU2yS5IVytK/4cWDIl79M978N6btHrT1wcDjvRlm5oUJZ9q47rdT2Njc2t4p7pb29g8Oj8rHJ10dp4pCh8Y8Vr2QaOBMQscww6GXKCAi5PAYTu7m/uMTKM1i2TbTBAJBRpJFjBJjJb91K6h/D9wQ3B6UK27NXQCvEy8nFZSjOSh/+cOYpgKkoZxo3ffcxAQZUYZRDrOSn2pICJ2QEfQtlUSADrLFzTN8YZUhjmJlSxq8UH9PZERoPRWh7RTEjPWqNxf/8/qpiW6CjMkkNSDpclGUcmxiPA8AD5kCavjUEkIVs7diOiaKUGNjKtkQvNWX10n3suZd1eqteqVRzeMoojN0jqrIQ9eogR5QE3UQRQl6Rq/ozUmdF+fd+Vi2Fpx85hT9gfP5Aw1UkPk=</latexit>
L = ↵L0 T
V = V0 T
Q = mc T
<latexit sha1_base64="wMhfKp9sHcpDZLkT4iLO3msba6g=">AAACEHicbVDLSsNAFJ3UV62vqEs3g0XsxpJIUTdCpZsuXFToC5oQJtNJO3TyYGYilJBPcOOvuHGhiFuX7vwbJ21AbT0wcOace7n3HjdiVEjD+NIKK6tr6xvFzdLW9s7unr5/0BVhzDHp4JCFvO8iQRgNSEdSyUg/4gT5LiM9d9LI/N494YKGQVtOI2L7aBRQj2IkleTop83ryY3lcYSTtmP5SI65nzTTs59PI02T29TRy0bVmAEuEzMnZZCj5eif1jDEsU8CiRkSYmAakbQTxCXFjKQlKxYkQniCRmSgaIB8IuxkdlAKT5QyhF7I1QsknKm/OxLkCzH1XVWZbSkWvUz8zxvE0ruyExpEsSQBng/yYgZlCLN04JBygiWbKoIwp2pXiMdIpSNVhiUVgrl48jLpnlfNi2rtrlauV/I4iuAIHIMKMMElqIMmaIEOwOABPIEX8Ko9as/am/Y+Ly1oec8h+APt4xtWcJ1d</latexit>
<latexit sha1_base64="vur8xc3fnlsqWE9v8n4p0rVXMdA=">AAAB83icbVDLSgNBEJyNrxhfUY9eBoOQU9iVoF6EQDx4TCAvSJYwO+kkQ2Znl5leISz5DS8eFPHqz3jzb5w8DppY0FBUddPdFcRSGHTdbyeztb2zu5fdzx0cHh2f5E/PWiZKNIcmj2SkOwEzIIWCJgqU0Ik1sDCQ0A4m1bnffgJtRKQaOI3BD9lIiaHgDK3Uq9+rau8BJDLa6OcLbsldgG4Sb0UKZIVaP//VG0Q8CUEhl8yYrufG6KdMo+ASZrleYiBmfMJG0LVUsRCMny5untErqwzoMNK2FNKF+nsiZaEx0zCwnSHDsVn35uJ/XjfB4Z2fChUnCIovFw0TSTGi8wDoQGjgKKeWMK6FvZXyMdOMo40pZ0Pw1l/eJK3rkndTKtfLhUpxFUeWXJBLUiQeuSUV8khqpEk4ickzeSVvTuK8OO/Ox7I146xmzskfOJ8/3VKQ2g==</latexit>
<latexit sha1_base64="P+3k29oz+dRzB1ze5Cix3NlT6d0=">AAAB73icbVA9SwNBEJ2LXzF+RS1tFoOQKtxJiDZCwMbCIgHzAckR9jZ7yZLdvXN3TwhH/oSNhSK2/h07/42b5ApNfDDweG+GmXlBzJk2rvvt5DY2t7Z38ruFvf2Dw6Pi8UlbR4kitEUiHqlugDXlTNKWYYbTbqwoFgGnnWByO/c7T1RpFskHM42pL/BIspARbKzUbd70Y4HE/aBYcivuAmideBkpQYbGoPjVH0YkEVQawrHWPc+NjZ9iZRjhdFboJ5rGmEzwiPYslVhQ7aeLe2fowipDFEbKljRoof6eSLHQeioC2ymwGetVby7+5/USE177KZNxYqgky0VhwpGJ0Px5NGSKEsOnlmCimL0VkTFWmBgbUcGG4K2+vE7alxWvVqk2q6V6OYsjD2dwDmXw4ArqcAcNaAEBDs/wCm/Oo/PivDsfy9ack82cwh84nz8xy49Z</latexit>
Q = nC T
Q = ±mL
H = kA
TH
TC
L
<latexit sha1_base64="1BdzY2cLSRcaxFAemNL06leOFZs=">AAACI3icbVDLSsNAFJ3UV62vqEs3wSJ0VRItKoJQcONGqNIXNKFMppN26EwSZyaFMuRf3PgrblwoxY0L/8VJm4VWDwwczrmXO+f4MSVC2vanUVhZXVvfKG6WtrZ3dvfM/YO2iBKOcAtFNOJdHwpMSYhbkkiKuzHHkPkUd/zxTeZ3JpgLEoVNOY2xx+AwJAFBUGqpb15N+splUI44U5yJNL12xSOXyg04ROps3EwVWxYftHiXpn2zbFftOay/xMlJGeRo9M2ZO4hQwnAoEYVC9Bw7lp6CXBJEcVpyE4FjiMZwiHuahpBh4al5xtQ60crACiKuXyitufpzQ0EmxJT5ejKLI5a9TPzP6yUyuPQUCeNE4hAtDgUJtWRkZYVZA8IxknSqCUSc6L9aaAR1EVLXWtIlOMuR/5L2adU5r9bua+V6Ja+jCI7AMagAB1yAOrgFDdACCDyBF/AG3o1n49WYGR+L0YKR7xyCXzC+vgEM9qbl</latexit>
<latexit sha1_base64="I5y3Run36cSojY8WvGrn8LTv4Jo=">AAACBXicbVDLSsNAFJ3UV62vqEtdBIvQVUlqUTdCwY3gpkpf0IQymU7aoTOTMDMRSsjGjb/ixoUibv0Hd/6NkzYLbT1w4XDOvdx7jx9RIpVtfxuFldW19Y3iZmlre2d3z9w/6MgwFgi3UUhD0fOhxJRw3FZEUdyLBIbMp7jrT64zv/uAhSQhb6lphD0GR5wEBEGlpYF5fDtwGVRjwRIl0is3EBAlZ2lSS/l9a2CW7ao9g7VMnJyUQY7mwPxyhyGKGeYKUShl37Ej5SVQKIIoTktuLHEE0QSOcF9TDhmWXjL7IrVOtTK0glDo4sqaqb8nEsiknDJfd2YXy0UvE//z+rEKLr2E8ChWmKP5oiCmlgqtLBJrSARGik41gUgQfauFxlAHoXRwJR2Cs/jyMunUqs55tX5XLzcqeRxFcAROQAU44AI0wA1ogjZA4BE8g1fwZjwZL8a78TFvLRj5zCH4A+PzB+AomL0=</latexit>
<latexit sha1_base64="Ke/s8InzU5BaA1lRkOLL/3yp9Dc=">AAAB7XicbVBNSwMxEJ2tX7V+VT16CRahp7Irol6EghePVdptoV1KNs22sdlkSbJCWfofvHhQxKv/x5v/xrTdg7Y+GHi8N8PMvDDhTBvX/XYKa+sbm1vF7dLO7t7+QfnwyNcyVYS2iORSdUKsKWeCtgwznHYSRXEcctoOx7czv/1ElWZSNM0koUGMh4JFjGBjJT/xb8RDs1+uuDV3DrRKvJxUIEejX/7qDSRJYyoM4VjrrucmJsiwMoxwOi31Uk0TTMZ4SLuWChxTHWTza6fozCoDFEllSxg0V39PZDjWehKHtjPGZqSXvZn4n9dNTXQdZEwkqaGCLBZFKUdGotnraMAUJYZPLMFEMXsrIiOsMDE2oJINwVt+eZX45zXvsnZxf1GpV/M4inACp1AFD66gDnfQgBYQeIRneIU3RzovzrvzsWgtOPnMMfyB8/kDFIKOvA==</latexit>
pV = nRT
<latexit sha1_base64="H/0/WvniF/rL0YEmUS3kqEAxkWM=">AAAB63icbVBNSwMxEJ2tX7V+VT16CRahp7IrpXoRCl68CBXsB7RLyabZNjTJLklWKEv/ghcPinj1D3nz35ht96CtDwYe780wMy+IOdPGdb+dwsbm1vZOcbe0t39weFQ+PunoKFGEtknEI9ULsKacSdo2zHDaixXFIuC0G0xvM7/7RJVmkXw0s5j6Ao8lCxnBJpPEjbwflituzV0ArRMvJxXI0RqWvwajiCSCSkM41rrvubHxU6wMI5zOS4NE0xiTKR7TvqUSC6r9dHHrHF1YZYTCSNmSBi3U3xMpFlrPRGA7BTYTvepl4n9ePzHhtZ8yGSeGSrJcFCYcmQhlj6MRU5QYPrMEE8XsrYhMsMLE2HhKNgRv9eV10rmseY1a/aFeaVbzOIpwBudQBQ+uoAl30II2EJjAM7zCmyOcF+fd+Vi2Fpx85hT+wPn8AbmIjfY=</latexit>
m = nM
3
Ktr = nRT
2
vrms =
r
<latexit sha1_base64="F/oef806RNAbz3nt1uSR4l5ry2c=">AAACFnicbVDJSgNBEO1xjXGLevQyGIR4SJiRoF6EiJccI2aDLENPpxKbdPcM3T1CGOYrvPgrXjwo4lW8+Td2FkETHxQ83quiqp4fMqq043xZS8srq2vrqY305tb2zm5mb7+ugkgSqJGABbLpYwWMCqhpqhk0QwmY+wwa/vB67DfuQSoaiKoehdDheCBonxKsjeRl8mUvbnOs7ySPBegkubyCtqIDjnPVbjFf9X7M26RbPPEyWafgTGAvEndGsmiGipf5bPcCEnEQmjCsVMt1Qt2JsdSUMEjS7UhBiMkQD6BlqMAcVCeevJXYx0bp2f1AmhLanqi/J2LMlRpx33SOj1Tz3lj8z2tFun/RiakIIw2CTBf1I2brwB5nZPeoBKLZyBBMJDW32uQOS0y0STJtQnDnX14k9dOCe1Yo3hSzpdwsjhQ6REcoh1x0jkqojCqohgh6QE/oBb1aj9az9Wa9T1uXrNnMAfoD6+MbLfSfSA==</latexit>
H = Ae T 4
<latexit sha1_base64="XoC/1cuOXstMHe3jJaAChcnB1Ro=">AAAB9XicbVBNSwMxEM3Wr1q/qh69BIvQU9mVol6EipceK/QL2m3JptM2NMkuSVYpS/+HFw+KePW/ePPfmLZ70NYHA4/3ZpiZF0ScaeO6305mY3Nreye7m9vbPzg8yh+fNHUYKwoNGvJQtQOigTMJDcMMh3akgIiAQyuY3M/91iMozUJZN9MIfEFGkg0ZJcZKvertHXQ1GwmC671yP19wS+4CeJ14KSmgFLV+/qs7CGksQBrKidYdz42MnxBlGOUwy3VjDRGhEzKCjqWSCNB+srh6hi+sMsDDUNmSBi/U3xMJEVpPRWA7BTFjverNxf+8TmyGN37CZBQbkHS5aBhzbEI8jwAPmAJq+NQSQhWzt2I6JopQY4PK2RC81ZfXSfOy5F2Vyg/lQqWYxpFFZ+gcFZGHrlEFVVENNRBFCj2jV/TmPDkvzrvzsWzNOOnMKfoD5/MHKg2Rkw==</latexit>
3kT
=
m
r
Hnet = Ae (T 4
<latexit sha1_base64="wSYHhvbq9lShYmygIqGPf8dfndE=">AAAB+XicbVBNS8NAEJ3Ur1q/oh69LBahp5KUol6EQi8eq9gPaEPYbDft0s0m7G4KJfSfePGgiFf/iTf/jds2B219MPB4b4aZeUHCmdKO820VtrZ3dveK+6WDw6PjE/v0rKPiVBLaJjGPZS/AinImaFszzWkvkRRHAafdYNJc+N0plYrF4knPEupFeCRYyAjWRvJtu+l37gahxCQL51lt/ujbZafqLIE2iZuTMuRo+fbXYBiTNKJCE46V6rtOor0MS80Ip/PSIFU0wWSCR7RvqMARVV62vHyOrowyRGEsTQmNlurviQxHSs2iwHRGWI/VurcQ//P6qQ5vvYyJJNVUkNWiMOVIx2gRAxoySYnmM0MwkczcisgYmxi0CatkQnDXX94knVrVva7WH+rlRiWPowgXcAkVcOEGGnAPLWgDgSk8wyu8WZn1Yr1bH6vWgpXPnMMfWJ8/G/WTQQ==</latexit>
3RT
M
CV =
f
R
2
TS4 )
<latexit sha1_base64="eSzr7b4JZeVsLnqSV20Xhoq/Bzg=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWARupCSlKJuhIIblxVsWmhimEwm7dDJJMxMhBLqxl9x40IRt/6FO//GaZuFth64l8M59zJzT5AyKpVlfRulldW19Y3yZmVre2d3z9w/cGSSCUw6OGGJ6AVIEkY56SiqGOmlgqA4YKQbjK6nfveBCEkTfqfGKfFiNOA0ohgpLfnmUffKpVz5uePbk3vdGxOYumeh45tVq27NAJeJXZAqKND2zS83THAWE64wQ1L2bStVXo6EopiRScXNJEkRHqEB6WvKUUykl88umMBTrYQwSoQuruBM/b2Ro1jKcRzoyRipoVz0puJ/Xj9T0aWXU55minA8fyjKGFQJnMYBQyoIVmysCcKC6r9CPEQCYaVDq+gQ7MWTl4nTqNvn9eZts9qqFXGUwTE4ATVggwvQAjegDToAg0fwDF7Bm/FkvBjvxsd8tGQUO4fgD4zPH0lZlhE=</latexit>
W =
Z
V2
<latexit sha1_base64="Ls9CX+YHkJJmMq6bdKVQ8dK5sUI=">AAAB8HicbVBNSwMxEJ2tX7V+VT16CRahIJRdKepFKPTisYr9kHZZsmm2DU2yS5IVSumv8OJBEa/+HG/+G9N2D9r6YODx3gwz88KEM21c99vJra1vbG7ltws7u3v7B8XDo5aOU0Vok8Q8Vp0Qa8qZpE3DDKedRFEsQk7b4ag+89tPVGkWywczTqgv8ECyiBFsrPRYD5KbetA6vw+KJbfizoFWiZeREmRoBMWvXj8mqaDSEI617npuYvwJVoYRTqeFXqppgskID2jXUokF1f5kfvAUnVmlj6JY2ZIGzdXfExMstB6L0HYKbIZ62ZuJ/3nd1ETX/oTJJDVUksWiKOXIxGj2PeozRYnhY0swUczeisgQK0yMzahgQ/CWX14lrYuKd1mp3lVLtXIWRx5O4BTK4MEV1OAWGtAEAgKe4RXeHOW8OO/Ox6I152Qzx/AHzucPj6qPhw==</latexit>
p dV
<latexit sha1_base64="pIriXmGMAWblBuvUjG8h4AoWk6g=">AAAB9XicbVDLSgNBEJz1GeMr6tHLYBByMexKUC9CQA8eE3CTQLKG2UlvMmT2wUyvEkL+w4sHRbz6L978GyfJHjSxoKGo6qa7y0+k0Gjb39bK6tr6xmZuK7+9s7u3Xzg4bOg4VRxcHstYtXymQYoIXBQooZUoYKEvoekPb6Z+8xGUFnF0j6MEvJD1IxEIztBID51bkMioS69p/azZLRTtsj0DXSZORookQ61b+Or0Yp6GECGXTOu2YyfojZlCwSVM8p1UQ8L4kPWhbWjEQtDeeHb1hJ4apUeDWJmKkM7U3xNjFmo9Cn3TGTIc6EVvKv7ntVMMrryxiJIUIeLzRUEqKcZ0GgHtCQUc5cgQxpUwt1I+YIpxNEHlTQjO4svLpHFedi7KlXqlWC1lceTIMTkhJeKQS1Ild6RGXMKJIs/klbxZT9aL9W59zFtXrGzmiPyB9fkDTPmRAg==</latexit>
Cp = CV + R
<latexit sha1_base64="Rh+GDW4himn2zedNh2Nj7w5rTnk=">AAACAHicbVBNS8NAEJ34WetX1IMHL4tF6KkkUtSLUKgHjxWattCGsNlu26WbTdjdCCX04l/x4kERr/4Mb/4bt20O2vpg4O17M+zMCxPOlHacb2ttfWNza7uwU9zd2z84tI+OWypOJaEeiXksOyFWlDNBPc00p51EUhyFnLbDcX3mtx+pVCwWTT1JqB/hoWADRrA2UmCf9u4o1xh56BaJetDKn83ALjkVZw60StyclCBHI7C/ev2YpBEVmnCsVNd1Eu1nWGpGOJ0We6miCSZjPKRdQwWOqPKz+QFTdGGUPhrE0pTQaK7+nshwpNQkCk1nhPVILXsz8T+vm+rBjZ8xkaSaCrL4aJBypGM0SwP1maRE84khmEhmdkVkhCUm2mRWNCG4yyevktZlxb2qVB+qpVo5j6MAZ3AOZXDhGmpwDw3wgMAUnuEV3qwn68V6tz4WrWtWPnMCf2B9/gBEfJTY</latexit>
U =Q
U = nCV
W
T
V1
<latexit sha1_base64="UQPbH/u+yeNkJ8DPZB0LrwdhJFw=">AAACAHicbVDLSsNAFL3xWesr6sKFm2ARuipJKepGKLhxWaUvaEKYTCft0MkkzEyEErLxV9y4UMStn+HOv3HaZqGtB+7lcM69zNwTJIxKZdvfxtr6xubWdmmnvLu3f3BoHh13ZZwKTDo4ZrHoB0gSRjnpKKoY6SeCoChgpBdMbmd+75EISWPeVtOEeBEacRpSjJSWfPO0d8Mf2i7jbigQzrp+PdfNyX2zYtfsOaxV4hSkAgVavvnlDmOcRoQrzJCUA8dOlJchoShmJC+7qSQJwhM0IgNNOYqI9LL5Abl1oZWhFcZCF1fWXP29kaFIymkU6MkIqbFc9mbif94gVeG1l1GepIpwvHgoTJmlYmuWhjWkgmDFppogLKj+q4XHSCehdGZlHYKzfPIq6dZrzmWtcd+oNKtFHCU4g3OoggNX0IQ7aEEHMOTwDK/wZjwZL8a78bEYXTOKnRP4A+PzBy5flhM=</latexit>
W = nRT ln
<latexit sha1_base64="0BP2Vg5HDAWwDN0TfzZ44Esggdo=">AAACDnicbZDNSsNAFIUn/tb4F3XpJlgK3VgSKepGKLhxWaFNC01aJtNJO3RmEmYmQgl9Aje+ihsXirh17c63cdpkoa0HBg7fvZc794QJJVI5zrextr6xubVd2jF39/YPDq2jY0/GqUC4jWIai24IJaaE47YiiuJuIjBkIcWdcHI7r3cesJAk5i01TXDA4IiTiCCoNBpYlcTr+yPIGLxBMZfK982W189ydO7Ocjqwyk7NWcheNW5hyqBQc2B9+cMYpQxzhSiUsuc6iQoyKBRBFM9MP5U4gWgCR7inLYcMyyBbnDOzK5oM7SgW+nFlL+jviQwyKacs1J0MqrFcrs3hf7VeqqLrICM8SRXmKF8UpdRWsT3Pxh4SgZGiU20gEkT/1UZjKCBSOkFTh+Aun7xqvIuae1mr39fLjWoRRwmcgjNQBS64Ag1wB5qgDRB4BM/gFbwZT8aL8W585K1rRjFzAv7I+PwBuw6b1g==</latexit>
pV
<latexit sha1_base64="Q0zmmL+d4ywvybEpv9KyehB8Y3s=">AAAB/3icbVDLSgMxFM3UV62vUcGNm2ARuiozUtSNUOjGZQX7gM4wZNJMG5pkhiQjlHEW/oobF4q49Tfc+Tem7Sy09cC9HM65l9ycMGFUacf5tkpr6xubW+Xtys7u3v6BfXjUVXEqMengmMWyHyJFGBWko6lmpJ9IgnjISC+ctGZ+74FIRWNxr6cJ8TkaCRpRjLSRAvvEGyHO0Y0XSYSzVpDkpnXzwK46dWcOuErcglRBgXZgf3nDGKecCI0ZUmrgOon2MyQ1xYzkFS9VJEF4gkZkYKhAnCg/m9+fw3OjDGEUS1NCw7n6eyNDXKkpD80kR3qslr2Z+J83SHV07WdUJKkmAi8eilIGdQxnYcAhlQRrNjUEYUnNrRCPkUlCm8gqJgR3+curpHtRdy/rjbtGtVkr4iiDU3AGasAFV6AJbkEbdAAGj+AZvII368l6sd6tj8VoySp2jsEfWJ8//U2WBA==</latexit>
=
Cp
CV
= const
<latexit sha1_base64="t1gJkLfHYhQ208mzvoScQxjPAJo=">AAACFXicbVBNS8NAEN3Ur1q/oh69BIsQQUtSinopFHrxWKVNC20Im+2mXbrZhN2NUEL+hBf/ihcPingVvPlv3LY5aOuDgcd7M8zM82NKhLSsb62wtr6xuVXcLu3s7u0f6IdHjogSjnAHRTTiPR8KTAnDHUkkxb2YYxj6FHf9SXPmdx8wFyRibTmNsRvCESMBQVAqydMvunXW9Byz7dmXba96Xh8EHKJUSVl6n5mxZzvKib2qo0xPL1sVaw5jldg5KYMcLU//GgwjlISYSUShEH3biqWbQi4JojgrDRKBY4gmcIT7ijIYYuGm868y40wpQyOIuComjbn6eyKFoRDT0FedIZRjsezNxP+8fiKDGzclLE4kZmixKEioISNjFpExJBwjSaeKQMSJutVAY6hikSrIkgrBXn55lTjVin1Vqd3Vyg0zj6MITsApMIENrkED3IIW6AAEHsEzeAVv2pP2or1rH4vWgpbPHIM/0D5/AEE+nE4=</latexit>
V2
V1
CV
(p1 V1 p2 V2 )
R
(depending on the process)
T V 1 = const
(adiabatic)
W = nCV (T1
T2 ) =
<latexit sha1_base64="sUg4xPo+5rkKLbYRJw38HzKFUV0=">AAACMnicbVDLSsNAFJ34tr6qLt0Ei+DGkkhRN4WCG90pWFtoQphMb9rByYOZG6Gk+SY3fongQheKuPUjnLYBtfXAwOGcc5l7j58IrtCyXoy5+YXFpeWV1dLa+sbmVnl751bFqWTQZLGIZdunCgSPoIkcBbQTCTT0BbT8u/OR37oHqXgc3eAgATekvYgHnFHUkle+hLoTSMqyVp5de05IsS/D7CLP6/aRIyDA4cT+8c7zqaQjea+PQ69csarWGOYssQtSIQWuvPKT041ZGkKETFClOraVoJtRiZwJyEtOqiCh7I72oKNpRENQbjY+OTcPtNI1g1jqF6E5Vn9PZDRUahD6OjnaVE17I/E/r5NicOZmPEpShIhNPgpSYWJsjvozu1wCQzHQhDLJ9a4m61NdEeqWS7oEe/rkWXJ7XLVPqrXrWqVxWNSxQvbIPjkkNjklDXJBrkiTMPJAnskbeTcejVfjw/icROeMYmaX/IHx9Q2kxKzL</latexit>
<latexit sha1_base64="QmDSqpxV5/dVuS3Mh9MnP47YL+4=">AAACK3icbVDLSsNAFJ3UV62vqEs3wSJ0Y0mkqBuh2E2XFfqCJoTJdNIOnUzCzEQoIf/jxl9xoQsfuPU/nLQRbeuBgTPn3Mu993gRJUKa5rtWWFvf2Nwqbpd2dvf2D/TDo64IY45wB4U05H0PCkwJwx1JJMX9iGMYeBT3vEkj83v3mAsSsracRtgJ4IgRnyAoleTqt9hN7ADKMQ+SBuQslGl6Y/scoqTt/hjN9Pz300jTBSt19bJZNWcwVomVkzLI0XL1Z3sYojjATCIKhRhYZiSdBHJJEMVpyY4FjiCawBEeKMpggIWTzG5NjTOlDA0/5OoxaczUvx0JDISYBp6qzFYUy14m/ucNYulfOwlhUSwxQ/NBfkwNGRpZcMaQcIwknSoCESdqVwONoQpKqnhLKgRr+eRV0r2oWpfV2l2tXK/kcRTBCTgFFWCBK1AHTdACHYDAA3gCr+BNe9RetA/tc15a0PKeY7AA7esbKhCqAw==</latexit>
W
e=
=1
QH
QC
QH
W = |QH |
<latexit sha1_base64="3Amx/1Rm0PUBSgr4CCdnqvbZokI=">AAACCHicbVDLSsNAFJ3UV62vqEsXBovQjSWRom6EQjddtmAf0IYwmU7aoTOTMDMRStqlG3/FjQtF3PoJ7vwbJ20WtfXAwJlz7uXee/yIEqls+8fIbWxube/kdwt7+weHR+bxSVuGsUC4hUIaiq4PJaaE45YiiuJuJDBkPsUdf1xL/c4jFpKE/EFNIuwyOOQkIAgqLXnmeed+2vT6DKqRYEl9Nr1a+tZmU88s2mV7DmudOBkpggwNz/zuD0IUM8wVolDKnmNHyk2gUARRPCv0Y4kjiMZwiHuacsiwdJP5ITPrUisDKwiFflxZc3W5I4FMygnzdWW6olz1UvE/rxer4M5NCI9ihTlaDApiaqnQSlOxBkRgpOhEE4gE0btaaAQFREpnV9AhOKsnr5P2ddm5KVealWK1lMWRB2fgApSAA25BFdRBA7QAAk/gBbyBd+PZeDU+jM9Fac7Iek7BHxhfv2LWmiY=</latexit>
|QC |
eCarnot =
<latexit sha1_base64="/5xA8KJIDC9WyxdGUQj6uFupNdY=">AAACCHicbVA9SwNBEN3zM8avqKWFi0FIFe5CUBshoIVlgvmCXAx7m71kyd7esTsnhCOljX/FxkIRW3+Cnf/GTXKFJj4YeLw3w8w8LxJcg21/Wyura+sbm5mt7PbO7t5+7uCwqcNYUdagoQhV2yOaCS5ZAzgI1o4UI4EnWMsbXU/91gNTmoeyDuOIdQMykNznlICRerkT94YJIPgOX2GXS+g59yXXV4Qm/dokqU96ubxdtGfAy8RJSR6lqPZyX24/pHHAJFBBtO44dgTdhCjgVLBJ1o01iwgdkQHrGCpJwHQ3mT0ywWdG6WM/VKYk4Jn6eyIhgdbjwDOdAYGhXvSm4n9eJwb/sptwGcXAJJ0v8mOBIcTTVHCfK0ZBjA0hVHFzK6ZDYmIAk13WhOAsvrxMmqWic14s18r5SiGNI4OO0SkqIAddoAq6RVXUQBQ9omf0it6sJ+vFerc+5q0rVjpzhP7A+vwBJsiYvg==</latexit>
<latexit sha1_base64="/b2SWnxZ1gIes9OvI0whplDSocI=">AAACDnicbVDLSsNAFJ3UV62vqEs3g6XQVUmkqFCEQjcFNy3YVmhCmEwn7dDJg5mJUNJ8gRt/xY0LRdy6duffOGmz0NYDFw7n3Mu997gRo0IaxrdW2Njc2t4p7pb29g8Oj/Tjk74IY45JD4cs5PcuEoTRgPQklYzcR5wg32Vk4E5bmT94IFzQMLiTs4jYPhoH1KMYSSU5euX2xvI4wsm86ySWj+SE+0nLaoTcarTTdJ4m88E8dfSyUTMWgOvEzEkZ5Og4+pc1CnHsk0BihoQYmkYk7QRxSTEjacmKBYkQnqIxGSoaIJ8IO1m8k8KKUkbQC7mqQMKF+nsiQb4QM99VndnBYtXLxP+8YSy9azuhQRRLEuDlIi9mUIYwywaOKCdYspkiCHOqboV4glQ6UiVYUiGYqy+vk/5Fzbys1bv1crOax1EEZ+AcVIEJrkATtEEH9AAGj+AZvII37Ul70d61j2VrQctnTsEfaJ8/WuGc4g==</latexit>
|QC or H |
K=
|W |
KCarnot =
for Cooling or Heating mode
<latexit sha1_base64="6wU+LZ7HUMrAkQqArcxOLvAyYgI=">AAACEXicbVDLSsNAFJ3UV62vqEs3wSJ0VRIpKnRT6KbLCrYVmlAm09t26EwmzEyEEvoLbvwVNy4UcevOnX/jpM1CWy8MnHvuY849Ycyo0q77bRU2Nre2d4q7pb39g8Mj+/ikq0QiCXSIYELeh1gBoxF0NNUM7mMJmIcMeuG0mdV7DyAVFdGdnsUQcDyO6IgSrA01sCs+x3oieToS0q83hTCLxn49S1pgerKEiyHMB3bZrbqLcNaBl4MyyqM9sL/8oSAJh0gThpXqe26sgxRLTQmDeclPFMSYTPEY+gZGmIMK0sVFc+fCMEPHaDIv0s6C/T2RYq7UjIemM9OvVmsZ+V+tn+jRTZDSKE40RGT50ShhjhZOZo8zpBKIZjMDMJHUaHXIBEtMtDGxZEzwVk9eB93LqndVrd3Wyo1KbkcRnaFzVEEeukYN1EJt1EEEPaJn9IrerCfrxXq3PpatBSufOUV/wvr8ARahnbs=</latexit>
<latexit sha1_base64="ZgV6GG9Y34WsjIFBh8ffl+dJxNk=">AAACVXicbVBdSxtBFJ1dv2JqG2Mf+7I0FHwKuyJtXwTBlz5aMCpkF5mZ3NXBmdl15m5qGOZ3+Gp/lfhjCk7iPpjYAxcO55zLvRxWS2ExTZ+jeG19Y3Ors939sPPxU2+3v3duq8ZwGPFKVuaSUQtSaBihQAmXtQGqmIQLdnsy9y+mYKyo9BnOaigUvdaiFJxikAp9lJeGcse9m/qr3UE6TBdI3pOsJQPS4vSqHx3kk4o3CjRySa0dZ2mNhaMGBZfgu3ljoab8ll7DOFBNFdjCLb72ybegTJKyMmE0Jgv17YajytqZYiGpKN7YVW8u/s8bN1j+LJzQdYOg+euhspEJVsm8gmQiDHCUs0AoNyL8mvAbGmrAUNTSFaZ8t5tr+MMrpaieuJyZKXA/zgqXB+JyhHtkpRtk3vuV5HKQqTYUWs5WO31Pzg+G2ffh4e/DwfF+23eHfCFfyT7JyA9yTH6RUzIinNyRB/JI/kZP0b94Pd58jcZRu/OZLCHuvQA/DLX7</latexit>
n=
<latexit sha1_base64="Z9dyocZBExdhxxqTbkjBQ00NNq8=">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</latexit>
c
v
S=
<latexit sha1_base64="Xz9+lYFOOd7i7tiG+TXzaajpi78=">AAACK3icbVDLSsNAFJ3UV62vqEs3wSJ0Y0mkqBuh2E3BTYW+oAlhMp20QyeTMDMRSsj/uPFXXOjCB279DydtENt6YODMOfdy7z1eRImQpvmhFdbWNza3itulnd29/QP98Kgrwpgj3EEhDXnfgwJTwnBHEklxP+IYBh7FPW/SyPzeA+aChKwtpxF2AjhixCcISiW5+u2dm9gBlGMeJA3IWSjT9Mb2OURJ2/010vTPr5meL1iuXjar5gzGKrFyUgY5Wq7+Yg9DFAeYSUShEAPLjKSTQC4Jojgt2bHAEUQTOMIDRRkMsHCS2a2pcaaUoeGHXD0mjZn6tyOBgRDTwFOV2Ypi2cvE/7xBLP1rJyEsiiVmaD7Ij6khQyMLzhgSjpGkU0Ug4kTtaqAxVEFJFW9JhWAtn7xKuhdV67Jau6+V65U8jiI4AaegAixwBeqgCVqgAxB4BM/gDbxrT9qr9ql9zUsLWt5zDBagff8A+Wqp5A==</latexit>
TC
TH
TC
<latexit sha1_base64="SZMPVtPq2zI3i8BqXiCMYgaB2ww=">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</latexit>
<latexit sha1_base64="FuvUR48v8rvuhnjmjLspjfcYl0U=">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</latexit>
0
=
y0
m=
=
y
n
<latexit sha1_base64="e0rA3CxWW+Sdq7j51fPc6CZ228E=">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</latexit>
na sin ✓a = nb sin ✓b
s0
s
R
f =
2
<latexit sha1_base64="obUuN25ckT140wpTeCogBDGwyKU=">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</latexit>
<latexit sha1_base64="k4y5l6YtDQiEYc094luL1P0K5OQ=">AAACunicbVHLbhMxFHWGVwmvFJZsLAKiEiiaQRXtAqRKbFihgpq2UmYU2Z47iRU/RranaWSZD+Br2MKf8Dd40hGQlCtZOj733DetBbcuTX/1khs3b92+s3O3f+/+g4ePBruPT61uDIMx00Kbc0osCK5g7LgTcF4bIJIKOKOLD63/7AKM5VqduFUNhSQzxSvOiIvUdPA8rwxhPgvehld/8cvw/s+nCtPBMB2la8PXQdaBIerseLrb+5qXmjUSlGOCWDvJ0toVnhjHmYDQzxsLNWELMoNJhIpIsIVfjxPwi8iUuNImPuXwmv03whNp7UrSqJTEze22ryX/55s0rjosPFd140Cxq0JVI7DTuN0NLrkB5sQqAsIMj71iNidxDS5ucKMKlRszeAVLd+ng0r1eo66DGTiLmdAW2hInPA6JP8ESf9GSKLycg8IKoISy389jHNMy8qXPqbkAFiZZ4fMIfN4mppUfZiGELeWmkMpOFC+Wbd/nOjh9M8rejvY/7w+P9rrb7aCn6BnaQxk6QEfoIzpGY8TQN/Qd/UA/k3cJTXiyuJImvS7mCdqwxP0GGpHcJQ==</latexit>
sin ✓crit =
1 1
1
+ 0 =
s s
f
<latexit sha1_base64="9ZXp2UE2SmO6F1YEkArjIKFsd4Y=">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</latexit>
nb
na
TC
TH
Z
2
1
dQ
T
<latexit sha1_base64="0z7ztVJZtoAN7Huhk6ZjxCoMV3c=">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</latexit>
<latexit sha1_base64="ABO92/aeV8mSfRPIdiKZM/oC+HM=">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</latexit>
I = Imax cos
1
= (n
f
Two-source Constructive Interference
TH
1
1)
R1
tan ✓p =
2
1
R2
!
<latexit sha1_base64="Fg6xd75ouNDVQjIV8Pr3NEpwnZA=">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</latexit>
M=
nb
na
✓ 0 25 cm
=
✓
f
Thin-film Reflection
2t = m
or
2t = (m + 12 )
<latexit sha1_base64="/EyyqudbPigHDzuPkR8R7+Kqu+8=">AAACoHicbZFNT9wwEIa96RdNv6A9crFYIXGoVglCtBckJC6cClQsoCYRcpzJroU/InvCsoqi/opey+/qv8FZcmCXjmTp0TvveMaevJLCYRT9GwQvXr56/Wbtbfju/YePn9Y3Pl84U1sOY26ksVc5cyCFhjEKlHBVWWAql3CZ3xx1+ctbsE4YfY7zCjLFJlqUgjP0UrKLByqV3l6w6/VhNIoWQZ9D3MOQ9HF6vTH4nRaG1wo0csmcS+KowqxhFgWX0IZp7aBi/IZNIPGomQKXNYuZW7rtlYKWxvqjkS7UpxUNU87NVe6diuHUreY68X+5pMbye9YIXdUImj82KmtJ0dDuA2ghLHCUcw+MW+FnpXzKLOPov2mpS67acPupoGGGdwh3+HVB/QgTQEe5NA66HufCv5L+gBn9aRTTdDYFTTVAAUUYpr6OG+X1oklzewu8TeKsST00aXdxXjbDuG3bFeeyMVe9ya8sXl3Qc7jYHcX7o72zveHhTr+8NbJJtsgOick3ckiOySkZE04M+UP+kvtgKzgOToKzR2sw6Gu+kKUIfj0Ah5nRDA==</latexit>
<latexit sha1_base64="V/qp1x3G95QdjQN5JUqDvFzkjWE=">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</latexit>
m = d sin ✓
<latexit sha1_base64="OECI4/GrLukULNbfPyRjgsc1NbY=">AAACq3icbZFNb9QwEIa94auEry1w42KxqtQDrBJUARekSlw4oQLdtmIdrRxnsmvVH5E96XaJIv4KV/hH/BucbQ7dLSNZevTOO56xJ6+U9JgkfwfRrdt37t7buR8/ePjo8ZPh7tMTb2snYCKssu4s5x6UNDBBiQrOKgdc5wpO8/OPXf70ApyX1hzjqoJM87mRpRQcgzQbPtdMBXfBPxTMS8NwAchnw1EyTtZBb0Law4j0cTTbHfxkhRW1BoNCce+naVJh1nCHUihoY1Z7qLg453OYBjRcg8+a9fgt3QtKQUvrwjFI1+r1ioZr71c6D07NceG3c534v9y0xvJ91khT1QhGXDUqa0XR0u4vaCEdCFSrAFw4GWalYsEdFxh+bKNLrtt477pgYImXCJf4ak39CHNAT4WyHroexzK8kn6GJf1qNTd0uQBDDUABRRyzUCesDnrRsNxdgGinadawAA3rLs7LZpS2bbvl3DTmujeFlaXbC7oJJ2/G6dvxwZeD0eF+v7wd8oK8JPskJe/IIflEjsiECPKD/CK/yZ/odfQt+h6xK2s06GuekY2I4B8LctVt</latexit>
m
d
ym = R
<latexit sha1_base64="kUwKn96vSZDwQBSvLf6TGuOnKPY=">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</latexit>
(Constructive or Destructive depending on relative phase shift)
(m = 0, ±1, ±2, ±3, ...)
<latexit sha1_base64="2n4yX2jyc6qCOgTXh2fyt9rIfTM=">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</latexit>
Single-slit Destructive
Diffraction
m
sin ✓ =
a
(m = ±1, ±2, ±3, ...)
<latexit sha1_base64="9Diqg0rnpVRLbEt6YLJxw5pT/rQ=">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</latexit>
(m = 0, 1, 2, 3, ...)
Diffraction Gratings
X-ray Diffraction
<latexit sha1_base64="AgfNA4MeQ44DC8+rAVtCxgGWY44=">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</latexit>
Circular Apertures
<latexit sha1_base64="oLf0bMPEZiuJyTlGUUz4mhywhB8=">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</latexit>
m = d sin ✓
<latexit sha1_base64="OECI4/GrLukULNbfPyRjgsc1NbY=">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</latexit>
<latexit sha1_base64="V0QpSczUl08yDUMo/nMtV8S5SMA=">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</latexit>
m = 2d sin ✓
<latexit sha1_base64="xCPSWeMHoKAHD/niNWgTpV8QXcA=">AAACsnicbVHLattAFB2rr1R9Oe0ym6Em4IIRVmrabgqBbroqaYmTUEuY0ejKHjIPMXMVxwhR+jXdtp/Tv+nI0SJ2emFmDueeO/eVlVI4HI//9oJ79x88fLT3OHzy9NnzF/39l2fOVJbDlBtp7EXGHEihYYoCJVyUFpjKJJxnl59a//kVWCeMPsV1CaliCy0KwRl6at4/GKqPSaloPGrvoxFtn7cjGkXRm3l/MI7GG6N3QdyBAensZL7f+5HkhlcKNHLJnJvF4xLTmlkUXEITJpWDkvFLtoCZh5opcGm96aKhh57JaWGsPxrphr0dUTPl3FplXqkYLt2uryX/55tVWHxIa6HLCkHzm0RFJSka2o6E5sICR7n2gHErfK2UL5llHP3gtrJkqgkPbxMaVniNcI2jDepKWAA6yqVx0OY4Fb5L+gVW9JtRTNPVEjTVADnkYZj4OG6U5/M6yewV8GYWp3XiQZ20H2dFPYibptlRbgsz1Yn8yuLdBd0FZ0dR/C6afJ0Mjofd8vbIAXlNhiQm78kx+UxOyJRw8pP8Ir/Jn2ASfA9YwG+kQa+LeUW2LJD/AArq1Lo=</latexit>
(m = 0, ±1, ±2, ±3, ...)
<latexit sha1_base64="2n4yX2jyc6qCOgTXh2fyt9rIfTM=">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</latexit>
<latexit sha1_base64="HT4XgzCW76mvFaxAe3xG6TGZiuk=">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</latexit>
(m = 1, 2, 3, ...)
sin ✓1 = 1.22
D
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