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One mole of an ideal monotomic gas at te...

One mole of an ideal monotomic gas at temperature `T_(0)` is expanding slowly while following the law `PV^(-1) =` constant. When the final temperature is `2T_(0)`, the heat supplied to the gas is `IRT_(0)`, where I is an integer. Find the value of I.

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The correct Answer is:
2
For process `PV^(x) =` constant, molar heat capacity is
`C = (R)/((gamma - 1)) + (R)/((1 - x))`
Gas is monatomic, `gamma = 5//3` and `x = -1`
So, `C = (R)/((5//3 - 1)) + (R)/((1 + 1)) = 2R`
`Delta Q = n C (Delta T) = (1) (2R) (2T_(0) - T_(0))`
`= 2RT_(0) = IRT_(0)` (given)
`I = 2`
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