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Oxygen gas is made to undergo a process ...

Oxygen gas is made to undergo a process in which its molar heat capacity `C` depends on its absolute temperature `T` as `C = alpha T`. Work done by it when heated from an initial temperature `T_(0)` to a final temperature `2 T_(0)`, will be

A

`4 alpha T_(0)^(2)`

B

`(alpha T_(0) - 1) (3T_(0))/2`

C

`(3 alpha T_(0) - 5) R T_(0)/2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
c
`C = C_(V) + W.`
where W. is the work done by the gas per unit mole per unit rise in temperature . So
`W. = alpha T - C_(V) = alpha T - (5R//2)`
` :. Delta W = int W. dT = underset(T_(0))overset(2T_(0))int (alpha T - (5R)/2) dT = (3 alpha T_(0) - 5R) T_(0)/2 `
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