Question

Consider a sample of ideal gas (0.50 moles) confined in a piston assembly that has diathermal walls (i.e. the walls allow heat exchange). The assembly is in contact with a thermal reservoir that holds the temperature constant at 300.K.

a) Suppose the ideal gas undergoes reversible isothermal compression from 25.0 L to 10.0 L. Calculate ΔS, ΔSsurrounding, and ΔStotal, where total = universe.

b) Suppose the ideal gas had instead been compressed isothermally by an external constant pressure from 25.0 L to 10.0 L. First determine the value of the minimum constant pressure for this process (in Pascals). Then, calculate ΔS, ΔSsurrounding, and ΔStotal.

Answer 1

a) Here, the process is an isothermal compression.

The heat released is given by

The initial volume is 25.0 L

The final volume is 10.0 L

Temperature is 300 K

n = 0.5 moles

R = 8.314 J/mol K

So,

The change in entropy of the system is given by

Since the process is reversible, the change total in entropy will be zero

So,

b) Here, the work done is equal to the heat released, since the temperature is kept constant.

If a constant pressure is applied to the piston, the work done on the piston is given by

Here, we are doing external work to the system instead of providing the heat Q. So, the heat absorbed/ released is zero. So,

The entropy change of the surroundings will be the same as before, since the work is done by the surroundings on the system.

So, total entropy change is