Question

In four experiments, 2.5 molof hydrogen gas undergoes reversible isothermal expansions, starting from the same volume but at different temperatures. The corresponding P-Vplots are shown in Fig. 20-21. Rank the situations according to the change in the entropy of the gas, greatest first.

Short answer

The ranking of the situations according to the change in entropy of the gas is$\Delta S_a=\Delta S_c>\Delta S_b=\Delta S_d$

Step-by-step solution

The given data

P-V plot for four different situations undergoing isothermal reversible process are given.

Understanding the concept of entropy change

Entropy change is a phenomenon that quantifies how disorder or randomness has changed in a thermodynamic system. Analyzing the given graph and using the formula for change in entropy for an isothermal reversible process we can rank the given situations according to the change in entropy of the gas.

Formulae:

The entropy change of a gas for the reversible process, $∆S=nRIn\frac{V_f}{V_i}$ …(i)

Calculation of the ranking of the situations according to entropy change

In the given plot,andhave the same initial and final volume. Also, b and d have same initial and final volume. Thus, entropy changes for paths can be given using equation (i) as follows:

$\Delta S_a=\Delta S_c$

$\Delta S_b=\Delta S_d$

Also, volume change for path a and c is greater than that for path b and d. Thus, the entropy change for paths a and c is also greater than that for paths b and d considering equation (i).

Therefore, ranking of the situations according to the change in entropy of the gas is $\Delta S_a=\Delta S_c>\Delta S_b=\Delta S_d$.