Solve Thermodynamics Problem: Expansion Irreversibly and Isothermally at 27°C

[sachin123]

Expansion irreversibly and isothermally of an ideal has from a volume of 2dm3 to 10 dm3 against a const pressure of 1 atm at 27 C .Find entropy change of the system and also surroundings due to the process.

Heres my attempt:
delta S=energy absorbed/temp
for the system,
= energy absorbed/temp=RTln(V2/V1)/T(as it is an isothermal exp)
putting in values I got,13.4J/K/mol
since energy absorbed by surroundings= -(energy absorbed by system)
delta S of surroundings= -13.4J/K/mol
My book gives different answer fro 2nd part.
Why am I wrong?
I just don't understand when we have to consider work and when not?(like for the system or the surroundings?)

 

[nate808]

Your attempt at finding the entropy change of the system is correct. However, the entropy change of the surroundings should also take into account the work done by the system on the surroundings. In this case, the system is doing work on the surroundings as it expands against a constant pressure. The work done by the system is given by W = PΔV, where P is the pressure and ΔV is the change in volume. In this case, ΔV = 8 dm3 = 8 L = 0.008 m3. Therefore, W = (1 atm)(0.008 m3) = 0.008 J.

The total entropy change of the surroundings is the sum of the energy absorbed by the surroundings and the work done by the system on the surroundings. Therefore, the entropy change of the surroundings is given by:

ΔS surroundings = ΔS energy + ΔS work

= (-13.4 J/K/mol) + (-0.008 J/K)

= -13.4 J/K/mol - 0.008 J/K

= -13.408 J/K/mol

This is the correct answer for the entropy change of the surroundings.

To answer your question about when to consider work, it is important to consider work whenever there is a change in volume or when there is a force acting on the system. In this case, the system is expanding against a constant pressure, so work must be considered. In other cases, such as an isothermal process with no change in volume, work may not need to be considered. It is important to carefully consider the process and determine if work needs to be taken into account in calculating entropy changes.