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Work Done in Reversible Adiabatic Process

If one mole o...

Question

If one mole of an ideal monoatomic gas at temperature $T_{0}$ is expanding slowly while following the law $P V^{- 1}$ = constant.
When the final temperature is $2 T_{0}$ , the heat supplied to the gas is $I R T_{0}$ , where I is an integer. Find the value of I.___

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Solution

For process $P V^{x}$ = constant
$C = \frac{R}{(γ - 1)} + \frac{R}{(1 - x)}$
For monoatomic, $γ = \frac{5}{3}, x = - 1$
C = 2R
$Δ Q = n C (Δ T) = 2 R T_{0} = I R T_{0} (g i v e n)$
I = 2

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