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Standard XII

Physics

Specific Heat Capacity

An ideal gas ...

Question

An ideal gas system undergoes an isothermal process, then the work done during the process is:

n R T l n \frac{V_{2}}{V_{1}}

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n R T l n \frac{V_{1}}{V_{2}}

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2 n R T l n \frac{V_{2}}{V_{1}}

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2 n R T l n \frac{V_{1}}{V_{2}}

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Solution

The correct option is A $n R T l n \frac{V_{2}}{V_{1}}$
Let an ideal gas goes isothermally from its initial state $(P_{1} V_{1})$ to the final state $(P_{2} V_{2})$ . Then the work done,

$W = \int_{V_{1}}^{V_{2}} P d V$

We have

$P V = n R T$

or

$P = \frac{n R T}{V}$

Then,

$W = \int_{V_{1}}^{V_{2}} \frac{n R T}{V} d V = n R T \int_{V_{1}}^{V_{2}} \frac{1}{V} d V$

$= n R T l n (V_{2}) - l n (V_{1}) = n R T l n \frac{V_{2}}{V_{1}}$

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An ideal gas system undergoes an isothermal process, then the work done during the process is:

The correct option is A nRTlnV2V1Let an ideal gas goes isothermally from its initial state (P1V1) to the final state (P2V2). Then the work done,W=∫V2V1PdVWe have PV=nRTorP=nRTVThen,W=∫V2V1nRTVdV=nRT∫V2V11VdV=nRTln(V2)−ln(V1)=nRTlnV2V1