Work done by a sample of an ideal gas in a process A is double the work done in another process B. The temperature rises through the same amount in the two processes. If `(C_A and C_B) be the molar heat capacities for the two processes,

Options

A. `C_A=C_B`
B. `C_A lt C_B`
C. `C_A gt C_B`
D. none

Answer

C

Explanation

`DeltaQ=DeltaU+DeltaW`
Process A: `DeltaQ=nC_ADeltaT=DeltaU+DeltaW`
Process B: `DeltaQ'=nC_BDeltaT=DeltaU+(DeltaW)/(2)`
`(i)//(ii)`
`(C_A)/(C_B)=(DeltaU+DeltaW)/(DeltaU+((DeltaW)/(2)))`
`C_A gt C_B`