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One mole of an ideal monoatomic gas at t...

One mole of an ideal monoatomic gas at temperature `T_0` expands slowly according to the law `p/V` = constant. If the final temperature is `2T_0`, heat supplied to the gas is

A

`2RT_(0)`

B

`RT_(0)`

C

`(3)/(2)RT_(0)`

D

`(1)/(2)RT_(0)`

Text Solution

Verified by Experts

The correct Answer is:
A
In a process `PV^(x)` = constant molar heat capacity is given by `C=(R )/(gamma-1)+(R )/(1-x)`
As the process is `(P)/(V)` = constant,
i.e `PV^(-1)`=constant , `threfore , x =-1`
For an ideal monatiomic gas , `gamma=(5)/(3)`
`C=(R )/((5)/(3)-1)+(R )/(1-(-1))=(3)/(2)R+(R)/(2)=2R`
`DeltaQ = n C(DeltaT)=1(2R)(2R_(0)-T_(0))=2RT_(0)`
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