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For polytropic process PV^(x) = constant...

For polytropic process `PV^(x)` = constant, molar heat capacity `(C_(m))` of an ideal gas is given by:

A

`C_(v,m)+(R)/((x-1))`

B

`C_(v, m)+(R)/((1-x))`

C

`C_(v,m)+R`

D

`C_(p,m)+(R)/((x-1))`

Text Solution

Verified by Experts

The correct Answer is:
B
`dU=dq+dw`
`nC_(v,m).dT=nC_(m).dT-P.dV`
`C_(m)=C_(v,m)+(P.dV)/(n.dT)` ….(1)
`PV^(n)=K and PV=nRT`
`therefore" "KV^(1-n)=nRT`
`K(1-n)V^(-n).dV=nRdT`
`(dV)/(dT)=(nR)/(K(1-n)V^(-n))` …(2)
from Eqs. (1) and (2)
`C_(m)=C_(v,m)+(R)/(1-n)`
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Knowledge Check

  • The density of the ideal gas is given by

    A
    `d=(PM)/(RT)`
    B
    `d=(RT)/(PM)`
    C
    `d=(PR)/(TM )`
    D
    `d=(PT)/(RM)`

  • The value of the molar mass constant ( R) for ideal gases is

    A
    0.2 cal/k
    B
    2cal/k
    C
    10cal/k
    D
    4.2cal

  • For an ideal gas C_(p) and C_(v) are related as

    A
    `C_(v) - C_(p) = R`
    B
    `C_(p) + C_(v) = R`
    C
    `C_(p) - C_(v) = R`
    D
    `C_(p) - C_(v) = RT`

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