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In a certain thermodynamic process the temperature of a gas is proportional to the squre of its pressure. The workdone by one mole of the gas when the temperature charges by $80 ° C$ will be $x$ R. $x$ =

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answer is 40.

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Detailed Solution

$T α P^{2} \Rightarrow P V α P^{2} \Rightarrow P V^{- 1} = C$

Polytropic exponent $x = - 1$

Now $W = \frac{n R}{1 - x} (T_{2} - T_{1}) = \frac{R}{1 - (- 1)} \times 80 = 40 R$

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