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

Options

A. `4 alpha T_(0)^(2)`
B. `(alphaT_(0) - 1) (3T_(0))/(2)`
C. `(3 alphaT_(0) - 5) (T_(0))/(2)`
D. None of these

Answer

C

Explanation

`C = C_(V)+W'` , where `W'` is the work done by the gas per unit mole per unit rise in temperature.
so, `W ' = alphaT-C_V =alphaT-(5R//2)`
`:. DeltaW = intW'dT=int_(T_0)^(2T_0)(alphaT-(5R)/(2))dT`
`=(3 alpha T_(0)-5)(T_0)/(2)`.