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A quantity of 2 mole of helium gas unde...

A quantity of 2 mole of helium gas undergoes a thermodynamic process, in which molar specific heat capacity of the gas depends on absolute temperature` T` , according to relation:
`C=(3RT)/(4T_(0)`
where `T_(0)` is initial temperature of gas. It is observed that when temperature is increased. volume of gas first decrease then increase. The total work done on the gas until it reaches minimum volume is :-

A

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

B

`(3)/(4)RT_(0)`

C

`(3)/(8)RT_(0)`

D

`(3)/(10)RT_(0)`

Text Solution

Verified by Experts

The correct Answer is:
B
When it reaches minimum volume, the process can be treated isochoric.
`(3RT)/(4T_(0)) = (3R)/(2)`
` T = 2T_(0)`
` DeltaQ = DeltaU + W`
`int_(T_(0))^(2T_(0))(2)(3RT)/(4T_(0))dT = (2)(3R)/(2)(2T_(0)-T_(0))+W`
` (6R)/(4T_(0))[T^(2)/(2)]_(T_(0))^(2T_(0))= 3RT _(0)+W`
` W=(9RT_(0))/(4)-3RT_(0)`
` W=-(3RT_(0))/(4)`
So work done on the gas `(3RT_(0))/(4)`
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Knowledge Check

  • Two moles of an ideal mono-atomic gas undergoes a thermodynamic process in which the molar heat capacity 'C' of the gas depends on absolute temperature as C=(RT)/(T_(0)) , where R is gas consant and T_(0) is the initial temperature of the gas. ( V_(0) is the initial of the gas). Then answer the following questions: The equation of process is

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    `1/P=(V_(0)T_(0)^(3//2))/(4RT^(5/2))e^((T-T_(0)/(T_(0)))`
    B
    `1/P=(V_(0)T_(0)^(3//2))/(2RT^(5/2))e^((T-T_(0)/(T_(0)))`
    C
    `1/P=(V_(0)T_(0)^(3//2))/(4RT^(5/2))e^((T+T_(0)/(T_(0)))`
    D
    `1/P=(V_(0)T_(0)^(3//2))/(3RT^(5/2))e^((T-T_(0)/(T_(0)))`

  • Two moles of an ideal mono-atomic gas undergoes a thermodynamic process in which the molar heat capacity 'C' of the gas depends on absolute temperature as C=(RT)/(T_(0)) , where R is gas consant and T_(0) is the initial temperature of the gas. ( V_(0) is the initial of the gas). Then answer the following questions: The minimum volume of gas is

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    `(2/3)^(3//2)V_(0)e^(1//2)`
    B
    `(4/3)^(3//2)V_(0)e^(1//2)`
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  • Oxygen gas is made to undergo a process in which its molar heat capacity C depends on its absolute temperature T as C = alpha T . Work done by it when heated from an initial temperature T_(0) to a final temperature 2 T_(0) , will be

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    `4 alpha T_(0)`
    B
    `(alpha T_(0) - R) (3 T_(0))/(2)`
    C
    `(3 alpha T_(0) - 5 R) (T_(0))/(2)`
    D
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