Question

Method 4 of W The temperature of n-moles of an ideal gas is increased from T_0 to 2T_0 through a process p=alpha/T. Find work done in this process.

Answer 1

Answer:

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Answer 2

Work done by the process = 2nR$T_0$

Given:

The temperature of n-moles of an ideal gas is increased from $T_0$ to 2$T_0$

Process p=$\frac{\alpha}{T}$

To find:

Work done in this process.

Formula used:

Ideal gas equation,

PV = nRT

Where,   P = Pressure

              V = Volume

              R = Characteristic gas constant

              T= Temperature

Work done by the process =  $\int_{V_{1}}^{V_{2}} p d V$

Explanation:

From ideal gas equation,

PV = nRT

$\frac{\alpha}{T}$ V = nRT

  V = $\frac{nRT^2}{\alpha}$

Differentiating above equation.

 dV = $\frac{2nRT}{\alpha}$

Work done by the process =  $\int_{V_{1}}^{V_{2}} p d V$

Putting value of pressure and dV

                                             = $\int_{T_{o}}^{2T_{0}} \frac{\alpha}{T} \ \frac{nRT^2}{\alpha}$

Work done by the process = 2nR$T_0$

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