1.

An ideal diatomic gas is expanded so that the amount of heat transferred to the gas is equal to the decrease in its internal energy. The molar specific heat of the gas in this process is given by `C` whose value isA. `-(5R)/(2)`B. `-(3R)/(2)`C. `2R`D. `(5R)/(2)`

Answer» Correct Answer - A
It is given that there is decrease in the internal energy while the gas expands absorbing some heat, which is numberically equal to the decrease in internal energy.
Hence, `dQ=-dU`
Thus, `dQ=dW+dU=-uD`
`dw=-2dU(` remembering that both `dW` and `dU` are negative `)`
`PdV=2CdT(dU=-CdT) ...(i)`
where `C` is the molar specific heat of the gas.
Since the gas is ideal , we have
`P=(RT)/(V) ....(ii)`
Hence Eq. (i) gives
`(RT)/(V) dV=2CdT`
`(dV)/(V)=(2C)/(R)(dT)/( T)`
Solving we get
`(VT^(2C//R))=` constant ....(iii)
Also since `dQ=-dU`,
`C=((dQ)/(dT))_("const ant volume")= ((dU)/(dT))=-C_(v)`
Hence,
`C=-C_(v)=(R)/( gamma-1)=-(R)/( (7)/(5)-1)=-(5R)/(2)`
Since the gas is diatomic.


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