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Q.

Two moles of an ideal monatomic gas are taken from state A to state B through a process as shown in figure. The work done by the gas in the process is

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a

$R (T_{2} - T_{1})$

b

$\frac{1}{4 R} (T_{2} - T_{1})$

c

$2 R (T_{2} - T_{1})$

d

$\frac{1}{2} R (T_{2} - T_{1})$

answer is A.

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Detailed Solution

$W = \int PdV and P = kV . Also (kV) V = 2 RT \Rightarrow V^{2} = \frac{2 RT}{k} Now W = \frac{k}{2} ({V_{2}}^{2} - {V_{1}}^{2}) = R (T_{2} - T_{1})$

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Two moles of an ideal monatomic gas are taken from state A to state B through a process as shown in figure. The work done by the gas in the process is