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Q.

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

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a

(3αT0-5)To2

b

(αTo-1)3T02

c

none of these

d

4αT02

answer is C.

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Detailed Solution

detailed_solution_thumbnail

C = Cv+W'; where W' is the work done by the gas per unit mole per unit rise in temperature

so,   W' = αT-Cv = αT-(5R2)dT 

 ∴   W' = ∫W'dT = ∫T02T0(αT - 5R2)dT

                = (3αTo-5)T02

 

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