Day 15, Physics 131
HW Problem 16-9
• A world record for the greatest change in
temperature was set in Spearfish, SD, on
January 22, 1943. At 7:30 a.m. the
temperature was -4.00oF; two minutes later
the temperature was 45oF.
• ? Find the average rate of temperature change
during those two minutes in Kelvins per
second. ??
HW Problem 16-19
• It is desired to slip an aluminum ring over a
steel bar. At 10.00oC the inside diameter of
the ring is 4.000 cm and the diameter of the
rod is 4.040 cm.
• ? (a) In order for the ring to slip over the bar,
should the ring be heated or cooled??
• ? (b) Find the temperature of the ring at which
it fits over the bar. The bar remains at 10.0oC
?
HW Problem 16-25
• An aluminum saucepan with a diameter of 23
cm and a height of 6.0 cm is filled to the brim
with water. The initial temperature of the
pan and water is 19oC. The pan is now placed
on a stove burner and heated to 88oC.
• Aaluminum = 24x10-6 K-1 bwater = 0.21x10-3 K-1
• ? (a) Will the water overflow from the pan ?
• ? (b) Calculate the volume of water that
overflows ??
HW Problem 16-27
• An exercise machine indicates that you have
worked off 2.5 Calories in a minute-and-a-half
of running in place.
• ? What was your power output during this
time ??
• Give you answer both in Watts and hp.
HW Problem 16-37
• Silver pellets with a mass of 1.0 g and a
temperature of 85oC are added to 220 g of water
at 14oC.
• ? (a) How many pellets must be added to increase
the equilibrium temperature of the system to
25oC ?
• ? (b) If copper pellets are used instead, does the
required number of pellets increase, decrease, or
stay the same ?
• ? (c) Find the number of copper pellets that are
required. ??
HW Problem 6-40
• A 97.6-g lead ball is dropped from rest from a
height of 4.57 m. The collision between the
ball and the ground is totally inelastic.
• ? Assuming all the ball’s kinetic energy goes
into heating the ball, find its change in
temperature. ??
HW Problem 6-51
• Assume: your skin temperature is 37.2 oC and
the temperature of your surroundings is
21.8 oC.
• ? Determine the length of time for you to
radiate away the energy gained by eating a
306-Calorie ice cream cone. ??
• Let the emissivity of your skin be 0.915 and its
area to be 1.22 m3.
HW Problem 16-76
• If heat is transferred to 150 g of water at a
constant rate for 2.5 minutes, its temperature
increases by 13 oC. When heat is transferred
at the same rate for the same amount of time
to a 150-g object of unknown material, its
temperature increases by 61 oC.
• ? (a) From what material is the object made. ?
• ? (b) What is the heating rate ??
HW Problem 16-92
• When the Blackbird lands, it is 8.0 inches
longer than it was at takeoff.
• Its coefficient of linear expansion is
22 x 10-6 K-1, and its temperature at
takeoff is 23oC.
• ? How hot is the Blackbird when it lands ??
Ideal Gas
• An Ideal Gas is a collection of atoms or
molecules that move randomly and exert no
long-range forces on each other. Each
particle of the ideal gas individually point-like,
occupying a negligible volume.
• A “mole” is a convenient measure.
• NA = 6.02 x 1023 particles/mole;
• NA = Avagadro’s number
Ideal Gas Law
•
•
•
•
•
•
•
Ideal Gas Law, PV = nRT
N = number of moles
T in Kelvin (K)
P in Pa
V in m3
R = 8.31 J/mole K
So – if one pumps up footballs in a sauna and then
takes then out to a cold, cold football game, what
happens to the pressure of the gas inside the balls?
Ideal Gas Example
•
•
•
•
•
•
•
4.50 L of ideal gas = 4.5 x 10-3 m3
Ti = 375 K
Tf = 275 K
V = constant
Pi = atmospheric pressure = 1.01 x 105 Pa
? (a) Pf = ?
? (b) n = ?
Sealed Container
• A sealed cubical container 20.0 cm on a side
contains three time Avagadro’s number of
molecules at a temperature of 20oC.
• ? Find the force exerted by the gas on one of
the walls of the container. ??
Internal Energy of Helium
• Helium has the special property that its
internal energy is directly proportional to its
absolute temperature. Consider a flask of
helium with a temperature of 2oC.
• ? If it is heated until it has twice the internal
energy, what will its temperature be ??
Deformation of Solids
• Stress = force per unit area causing
deformation
• Strain = increase in the amount of
deformation
• For small stress, stress = (elastic
modulus)*(strain)
• Recall: F = k Dx , Hooke’s Law for springs
Stress/Strain
•
•
•
•
•
•
Tensile Stress defined as F/A
Units of stress are N/m2 = Pascal (Pa)
Tensile Strain defined as DL/Lo
Tensile Strain is unitless
F/A = Y * (DL/Lo)
Young’s Modulus, Y, table on page 585
Bulk Modulus – Volume Elasticity
• Volume Stress DP
• DP = -B DV/V
Steel Wire
• Given: the elastic limit of steel is 5.0 x 108 Pa.
• Given: circus performer has mass 70 kg.
• ? What is the minimum diameter of a steel
wire used to support the performer ??
Latent Heats
• Latent Heat = L = Q / m (notice no DT)
• Latent Heat of Fusion, Lf, the latent heat to
melt (or fuse) a substance.
• Latent Heat of vaporization, Lv is the latent
heat required to convent a liquid to a gas.
• … and, recalling the recent winter snow, …
• Latent Heat of Sublimation is the latent heat
needed to convent a solid directly to a gas.
Heat and Phase Transfers
• The most important information for today is the figure on the top of page
596.
• It shows
• A. Heating ice, for which you need cice
• B. Melting ice, for which you need Lf of ice
• C. Heating water, for which you need cwater
• D. Converting water to steam, for which you need Lv of water
• E. Heating steam, for which you need csteam.
Temperature vs heat added or removed
A Lead Bullet
• Suppose a lead bullet with a mass of 5.00 g
and initial temperature of 65oC hits a wall and
completely liquifies.
• ? What minimum speed did it have before
impact ??
• Assume lead melting temp is 327.3oC
• Assume specific heat of lead is 128 J/kg*K
• Assume latent heat of fusion of lead is 2.45 x
104 J/kg.
Party Time
• At a party, 6.00 kg of ice at -5.00oC is added to
a cooler holding 30 liters of water at 20.0oC.
• ? What is the temperature of the water when
it comes to equilibrium ?
The Laws of Thermodynamics
• Zeroth: If object A is in thermal equilibrium
with object C, and object B is separately in
thermal equilibrium with object C, and objects
A and B will be in thermal equilibrium if they
are placed in thermal contact.
• First: The change in a system’s internal
energy, DU, is related to the heat Q and the
work W as follows:
DU = Q - W
Laws of Thermodynamics
• Second: When object of different
temperatures are brought into thermal
contact, the spontaneous flow of heat that
results is always from the high-temperature
object to the low-temperature object.
Spontaneous heat flow never proceeds in the
reverse direction.
Carnot Engine
• The efficiency of a Carnot engine,
ec = 1 – (Tc/Th) T in K in Kelvin !!!
• *****No real engine operating between two
energy reservoirs can be more efficient than a
Carnot engine operating between the same
two reservoirs.******
Heat Engine example
• A Carnot engine is operating between a hot
temperature, Thot of 100oC and a cold
temperature , Tcold of 20oC.
• ? What is the maximum possible efficiency of
this engine ??
• ? If Thot = 500oC, what is the maximum
possible efficiency ??
Power Plant
• A power plant has been proposed that would
make use of the temperature gradient in the
ocean. The system is to operated between
20.0oC (surface water temperature) and 5.00oC
(water temperature at a depth of about 1 km).
• ? (a) What is the maximum efficiency of such a
system. ??
• ? (b) If the useful power output of the plant is
75.0 MW, how much energy is absorbed per
hour?