Heat
Summary
Energy Balance: For a general system, ΔE = Q + W.
Expanding this to specify input and output,
ΔE = Qin + Win – Qout - Wout
Many devices, such as engines and refrigerators, have no internal ΔE, giving
Qin + Win = Qout - Wout
Win = 0 for a heat engine; Wout = 0 for a refrigerator or heat pump.
Efficiency = desired output
input needed
Carnot efficiency, for ΔS = 0, in terms of T’s
Heat engine eff. = Wout/Qin
Carnot eff. = (TH-TC)/TH
Refrigerator : eff. = Qin/Win
Heat Pump: “eff” = Qout/Win > 1
Entropy (S) :
ΔSuniverse > 0 for any process
S = Q/T
also true for any other isolated system.
equivalent statements:
Heat flows from higher temperature to lower temperature.
No heat engine can be 100% efficient.
Systems tend toward more disorder (more probable arrangements).
The forward direction for time is the direction of increasing entropy
(more probable).
It is impossible to reach absolute zero.
Temperature (T) :
T (K) = °C + 273, = 0 at absolute 0 (no molecular motion left).
Temperature is a measure of the average random kinetic energy.
3/2 kT = (avg KE)/particle or 3/2 RT = (avg KE)/mole
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The net transfer of heat stops when two objects have the same
temperature (Thermal Equilibrium)
Pressure (P)
Pressure is the force per unit area caused by molecular collisions.
By using the relationship between Temperature and KE, one gets the
Ideal Gas Law:
PV = nRT (in moles)
= NkBT (in particles)
R = 8.314 J/molK = .0821 Latm/ molK
kB= R/NA
NA = 6.023 x 1023
1 atmosphere = 760 mm Hg = 101.3 kPa 1Pa = 1 N/m2
Processes are often represented on a PV diagram.
The work done by a gas is equal to the area under the PV curve for the
process. The sign (+/-) is determined by the direction of the process on the
graph:
During expansion, the gas does work on the surroundings,
work done on the gas is negative or work done by the gas is positive.
During compression, work is done on the gas by the surroundings,
work done on the gas is positive or work done by the gas is negative.
No work is done if the volume doesn’t change during a process; but heat will
be transferred! For such processes, use the ideal gas equation to get the
temperatures and then the heat can be determined from the ΔT.
T = PV/(nR) for each point on the PV plot.
ΔT = Tf - Ti
Q = n C ΔT = n (3/2 R) ΔT = 3/2 nR ΔT
Q = 3/2 nR ΔT
At constant volume:
CV(monatomic gas) = 3/2 R per mole
CV(diatomic gas) = 5/2 R per mole
CP(monatomic gas) = 5/2 R per mole (extra R per mole for PV work)
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Heat transfer by:
Conduction: collisions of particles at contact surface transfers
random KE until avg KE’s are equal (equal temperature = thermal equilibrium)
Q/t = k (A/thickness) ΔT
Convection : heat transferred to fluid, moving fluid carries heat away.
Radiation : heat is transferred from a hot object as emitted “light” or
electromagnetic radiation.
Q/t = eσAT4 hot objects emit radiation most efficiently.
Calorimetry:
Qgained = Qlost
Q = mcΔT + mL ; temperature change with specific heat c;
latent heat for phase transformation = L per gram.
Thermal expansion:
ΔL = α L ΔT
ΔV = β V ΔT
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Fluids:
Pressure due to collisions,
Pressure in an enclosed sample in equilibrium the same
anywhere along a horizontal surface.
Pressure has no direction.
P = Po + ρgh
Archimedes’ Principle: A floating object displaces a mass of fluid equal to its
own mass.
If a fraction, f, of an object is submerged in a fluid, then
f ρ(fluid) = ρ(object) = average density of whole object.
If an object sinks, but is weighed in air and in a liquid;
(mass in air)/ Δm (water) = ρ(object)
Δm (liquid)/V(object) = ρ(liquid)
For incompressible flow,
A1v1 = A2v2
P1 + ρgh1 + ½ ρv12 = P2 + ρgh2 + ½ ρv22
streamlines don’t cross, closer together = faster flow
Viscous flow:
v A = π R4 ΔP/(8 η L) η = viscosity
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