First slide

Thermodynamic processes

Question

A gas expands with temperature according to the relation $V = K T^{\frac{2}{3}}$ .What is the work done when the temperature changes by 30⁰C

Moderate

A

10R
B

30R
C

50R
D

20R

Solution

In polytrophic process
$\begin{array}{l} T V^{n - 1} = K \\ V = K T^{(\frac{- 1}{n - 1})} \\ Given V = K T^{\frac{2}{3}} \\ \frac{- 1}{n - 1} = \frac{2}{3} \\ 2 n - 2 = - 3 \\ 2 n = - 1 \\ n = - \frac{1}{2} \\ W = \frac{R}{1 - n} (T_{2} - T_{1}) \\ W = \frac{R}{1 + \frac{1}{2}} (30) \\ W = 20 R \end{array}$

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