TP4: Thermodynamics and Statistical Physics
WS 2015/16
Worksheet 2
30.10.15
First law of thermodynamics
We continue our investigation of gases (ideal and photon gases) and extend it to work, heat and
the first law of thermodynamics.
Exercise 5: Expansion of an ideal gas 1
Preparation for the first law.
One mole of an ideal gas expands quasistatically at constant temperature, T = 20◦ C, from an
initial pressure of 20atm to a final pressure of 1atm (1 atm= 1.013 × 105 Pa).
a) How much work is done by the gas?
b) How much heat is absorbed by the gas?
Exercise 6: Photon gas
In thermodynamics blackbody radiation is usually described using a photon gas.
a) Use the first law of thermodynamics to show that for an adiabatic transformation:
∂U
P + ∂V
dP
P
=−
∂U
dV
∂P V
b) The internal energy of a photon gas is U = 3P V . Show that for an adiabatic transformation
P V γ = const. Determine the adiabatic exponent γ.
c) The equation of state of a photon gas is P = σT 4 /3 where σ is the Stefan-Boltzmann constant. How is an isothermal process characterized in the P V plane? Plot an adiabatic and an
isothermal transformation in the P V plane.
Exercise 7: Expansion of an ideal gas 2
Application of the first law.
Calculate heat and work when the volume of an ideal gas is doubled during an isothermal and isobaric transformation where T0 and V0 are the initial temperature and initial volume, respectively.
Exercise 8: State transformation for different processes
Energy is a state function and thus process independent.
An ideal gas is brought quasistatically from state {P1 , V1 , T1 } to state {P2 , V2 , T2 } in three different
ways:
a) 1A2
b) 1B2
c) 1DC2
For each process 1 → 2, evaluate internal energy, work and heat assuming that the heat capacity
is constant (δQ = CV,P dT with CP − CV = nR and CV = 3nR/2).
For the adiabatic process P V γ = const, (see exercise 6), compute the adiabatic exponent γ for
the ideal gas using U (T ) = 3nRT /2.