For an ideal gas, consider the molar volume Vm = (V/n) =
Vm(T,P). In other words, the molar volume is a function of
temperature and pressure.
a) Write the total differential dVm.
b) Show that dVm is exact.
c) Derive an expression for the differential work dw performed
in a reversible process by expansion/compression of the gas.
d) Show that dw is inexact.
e) What is the thermodynamic significance of having an exact
For 1 mol of an ideal gas, Pexternal = P = 1 atm. The
temperature is changed from 125ºC to 25.0ºC, and CV,m = 3/2R.
Calculate (all units are J) q= , w= , ∆U= , and ∆H= . Please enter
your answers with 2 decimals in E notation, such as 2.33E4
(=23345). If the answer is negative, please do not forget the
negative sign. If answer is zero, please just enter 0 without
One mole of an ideal gas in an initial state P = 10atm, V = 5L,
is taken reversibly in aclockwise direction around a circular path
given by (V − 10)^2 + (P − 10)^2 = 25. Computethe amount of work
done by the gas and the change in internal energy.
Ideal gas is expanded keeping (a) P V 2=const, (b) P
2V =const. Do these processes lead to temperature
increase or to temperature decrease? Find the specific heat
capacities for the gas during these processes.
A sample of an ideal gas at 1.00 atm and a volume of 1.46 L was
placed in a weighted balloon and dropped into the ocean. As the
sample descended, the water pressure compressed the balloon and
reduced its volume. When the pressure had increased to 10.0 atm,
what was the volume of the sample? Assume that the temperature was