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The molar heat capacity in a process of ...

The molar heat capacity in a process of a diatomic gas if it does a work of `Q/4` when a heat of `Q` is supplied to it is

A

`(2)/(5)R`

B

`(5)/(2)R`

C

`(10)/(3)R`

D

`(6)/(7)R`

Text Solution

Verified by Experts

The correct Answer is:
c

`dU=C_(v)dT=((5)/(2)R)dT`
`rArr dT=(2(dU))/(5R)`
From first law of thermodynamics, `dU=dQ=dW`
or `dU=Q-(Q)/(4)=(3Q)/(4)`
Now, molar heat capacity.
`C=(dQ)/(dT)=(Q)/(2((dU)/(5R)))=(5QR)/(2((3Q)/(4)))=(10)/(3)R`
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Knowledge Check

  • The molar heat capacity of a gas in a process

    A
    is either `C_(V) or C_(P)`
    B
    lies between `C_(V) or C_(P)`
    C
    may range from zero to infinity
    D
    can have any real value
  • Molar heat capacity of a gas is

    A
    Extensive property
    B
    Intensive property
    C
    Chemical property of gas
    D
    Colligative property
  • The molar heat capacity for the process shown in fig. is

    A
    `C=C_(v)`
    B
    `C=C_(p)`
    C
    `C gt C_(v)`
    D
    `C lt C_(v)`
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