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Expert-verified Found in: Page 604 ### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718 # A gas sample undergoes a reversible isothermal expansion. Figure gives the change ${\mathbf{∆}}{\mathbit{S}}$ in entropy of the gas versus the final volume ${{\mathbit{V}}}_{{\mathbf{f}}}$of the gas. The scale of the vertical axis is set by ${\mathbf{∆}}{{\mathbit{S}}}_{{\mathbf{s}}}{\mathbf{=}}{\mathbf{64}}{\mathbf{}}{\mathbf{J}}{\mathbf{/}}{\mathbf{K}}$. How many moles are in the sample? The number of moles in the sample is 3.5 mol.

See the step by step solution

## Step 1: The given data

a) The entropy change of the gas sample, $∆{S}_{s}=64\mathrm{J}/\mathrm{K}$

b) The graph of entropy change $∆S$and volume ${V}_{f}$is given.

## Step 2: Understanding the concept of entropy change

Entropy change is a phenomenon that quantifies how disorder or randomness has changed in a thermodynamic system. We can write the expression for the number of moles by rearranging the formula for entropy change. Then by inserting the values obtained from the given graph, we can find the number of moles in the gas sample.

Formulae:

The entropy change of the gas, $∆S=nRIn\left(\frac{{V}_{f}}{{V}_{i}}\right)-n{C}_{v}In\left(\frac{{T}_{f}}{{T}_{i}}\right)$ …(i)

## Step 3: Calculation of the number of moles in the sample

In an isothermal process, the temperature value remains constant. So, ${T}_{f}={T}_{i}$

Thus, using equation (i), we can get the number of moles present in the gas sample is given as follows:

(From the graph, we can infer that,$∆S=32\frac{\mathrm{J}}{\mathrm{K}},{V}_{f}=1.2{\mathrm{m}}^{3},{\mathrm{V}}_{\mathrm{i}}=0.4{\mathrm{m}}^{3}.$)

Hence, there are 3.5mol present in the gas sample. ### Want to see more solutions like these? 