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Method 4 of W The temperature of n-mol...

Method 4 of W
The temperature of n-moles of an ideal gas is increased from `T_0` to `2T_0` through a process `p=alpha/T`. Find work done in this process.

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The correct Answer is:
B
`pV=nRT` (ideal gas equation) …(i)
and `p=alpha/T` …(ii)
Dividing Eq. (i) by Eq. (ii), we get
`V=(nRT^2)/(alpha` or `dV=(2nRT)/(alpha)dT`
`:.` `W=int_(V_i)^(V_f)pdV=int_(T_0)^(2T_0)(alpha/T)((2nRT)/(alpha))dT`
`=2nRT_0`
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