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One mole of an ideal gas passes through ...

One mole of an ideal gas passes through a process where pressure and volume obey the relation `P=P_0 [1-1/2 (V_0/V)^2]` Here `P_0` and `V_0` are constants. Calculate the change in the temperature of the gas if its volume changes from `V_0` to `2V_0`.

A

`5/4 (P_0V_0)/(R)`

B

`1/4(P_0V_0)/(R)`

C

`3/4 (P_0V_0)/(R)`

D

`1/2 (P_0V_0)/(R)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(nRT)/(V)=P_0[1-1/2((V_0)/(V))^2]`
`T=(P_0V)/(R)(1-1/2((V_0)/(V))^2]`
`T_i=(P_0V)/(R) (1-1/2(V_0^2)/(v^2))=(P_0V_0)/(2R)`
`T_f=(P_02V)/(R)(1-(V_0^2)/(8V^2))=7/4 (P_0V_0)/(R)`
`Delta T=T_f-T_i=7/4 (P_0V)/(R)-(P_0V_0)/(2R)=5/4 (P_0V_0)/(R)`
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