The temperature of n moles of an ideal gas is increased from T to 4T through a process for which pressure $P = a T^{- 1}$ where a is a constant. Then, the work done by the gas is

nRT

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4nRT

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2nRT

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6nRT

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Solution

The correct option is D 6nRT
Given,
$P = a T^{- 1}$
$P = \frac{a}{T}$
From ideal gas equation,
$P V = n R T$
$V = \frac{n R T}{P} = \frac{n R T^{2}}{a}$
$d V = \frac{2 n R T}{a} d T$
Work done by the gas, $d W = P d V$
$W = \int_{T}^{4 T} (\frac{a}{T} . \frac{2 n R T}{a} d T)$
$W = 2 n R \int_{T}^{4 T} d T = 2 n R [T]_{T}^{4 T}$
$W = 2 n R (4 T - T)$
$W = 2 n R \times 3 T$
$W = 6 n R T$
The correct option is D.

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The temperature of n moles of an ideal gas is increased from T to 4T through a process for which pressure P=aT−1 where a is a constant. Then, the work done by the gas is

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The temperature of n moles of an ideal gas is increased from T to 4T through a process for which pressure $P = a T^{- 1}$ where a is a constant. Then, the work done by the gas is