Question

A gas, confined to an insulated cylinder, is compressed adiabatically to half its volume. Does the entropy of the gas increase, decrease, or remain unchanged during this process?

Short answer

The entropy of the gas remains unchanged during adiabatic compression.

Step-by-step solution

The given data

A gas is compressed adiabatically to half its volume in an insulated cylinder, $V_f=\frac{1}{2}{V}_i$.

Understanding the concept of entropy change

Entropy change is a phenomenon that quantifies how disorder or randomness has changed in a thermodynamic system. Using the condition for adiabatic processes in the formula for entropy change, we can predict the change in entropy.

Formulae:

The entropy change for a gas, $∆S={\int }_i^f\frac{dQ}{T}=\frac{Q}{T}$ …(i)

Calculation of the entropy change in adiabatic expansion

This is an adiabatic compression. Adiabatic is the process in which heat is exchanged by the system with the surrounding or vice versa.

Hence,$dQ=0$

Thus, using equation (i), we can get the change in entropy during its expansion as follows:$∆S=0$

Therefore, the change in entropy remains unchanged.