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1. Obtain an expression for work done in an isothermal process.

1. Obtain an expression for work done in an isothermal process.

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear Vaibhav
 
Analytical Method

Analytically, we can be calculated by integrating dW between the limits V1 to V2.

W=\int_{0}^{W}dW=\int_{v_1}^{v_2}PdVFor a perfect gas, PV = RT or P = RT/V

Substituting P = RT/V in the above equation, we get,

W = \int_{V^{_{1}}}^{V_{2}}\frac{RT}{V} dV

As temperature is constant during isothermal expansion and R is a gas constant,

W =RT \int_{V^{_{1}}}^{V_{2}}\frac{dV}{V} = RT [log_{e}V]_{V_{1}}^{V_{2}}

= RT (logeV2 -logeV1)

= RT loge (V2/V1)

Regards

Arun (askIITians forum expert)

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