Question

Question No: 1. A system is undergoing expansion with Pop = p (pressure of the gas); then multistage compression with Pop = P. The initial and final volume for the expansion process are V i and Vf, respectively. The initial and final volume for the compression are Vf and Vi, respectively. Calculate the net work done in the whole process

Answer 1

Answer on the question #61927, Chemistry / Physical Chemistry

Question:

Question No: 1. A system is undergoing expansion with Pop = p (pressure of the gas); then multistage compression with Pop = P. The initial and final volume for the expansion process are V i and Vf, respectively. The initial and final volume for the compression are Vf and Vi, respectively. Calculate the net work done in the whole process

Solution:

Isobaric expansion or compression work, done by the system, can be expressed as:

$$W = - p \Delta V.$$

Then, for the expansion part, we can write the following:

$$W _ {1} = - p \Delta V = - p \left(V _ {f} - V _ {i}\right).$$

For the compression stage, analogical expression:

$$W _ {2} = - p \Delta V = - P \left(V _ {i} - V _ {f}\right).$$

The net work done by the system in the whole process is

$$W = W _ {1} + W _ {2} = - p \left(V _ {f} - V _ {i}\right) - P \left(V _ {i} - V _ {f}\right) = \left(V _ {i} - V _ {f}\right) (p - P).$$

Answer: $(V_{i} - V_{f})(p - P)$

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