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In an adiabatic change, the pressure and...

In an adiabatic change, the pressure and temperature of a monoatomic gas are related with relation as `P prop T^(C )`, Where `C` is equal to:

A

`5/4`

B

`5/3`

C

`3/5`

D

`5/2`

Text Solution

Verified by Experts

The correct Answer is:
D
For adiabatic process
`PV^(gamma)` constant ..(i)
We have ideal gas relation , `PV=RT`
`implies V = (RT)/(P) `...(ii)
From equ. (i) and (ii) we get
`P((RT)/(P))^(gamma)` = constant
`implies (T^(gamma))/(P^(gamma-1)) = consta nt` ..(iii)
where `gamma` is adiabatic consta nt of the gas
Given `P prop T^(C)` ...(iv)
On comparing with eq, (iii) we have
`C = (gamma)/(gamma-1)`
For a monoatomic gas `gamma=5/3`
`:.` we have , `C = (5/3)/(5/3-1) = 5/2`.
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Knowledge Check

  • In an adiabatic change, the pressure and temperature of a monatomic gas are related as P prop T^0 , where c equals

    A
    `3/5`
    B
    `5/3`
    C
    `2/5`
    D
    `5/2`

  • In an adiabatic change, the pressure p and temperature T of a diatomic gas are related by the relation ppropT^alpha , where alpha equals

    A
    (a) 1.67
    B
    (b) 0.4
    C
    (c) 0.6
    D
    (d) 3.5

  • Relation between pressure (p) and energy (E) of a gas is

    A
    `p = (2)/(3) E`
    B
    `p = (1)/(3) E`
    C
    `p = (3)/(2) E`
    D
    `p = 3 E`

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