First slide

First law of thermodynamics

Question

In a process $V \propto T^{3}$ , temperature of one mole of a gas is increased by 200k work done by the gas in this process will be

Difficult

A

600 R
B

800 R
C

1000 R
D

1200 R

Solution

$\begin{array}{l} V = K T^{3}, d V = 3 K T^{2} d T \\ W = \int P d V = \int \frac{n R T}{V} d V = \int \frac{n R T}{V} 3 k T^{2} d T \\ \int 3 n R d T = 3 R (200) = 600 R \end{array}$

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