Statement - I : When μ amount of an ideal gas undergoes adiabatic change from state P 1 , V 1 , T 1 to…

Statement - I : When μ amount of an ideal gas undergoes adiabatic change from state P1,V1,T1 to state P2,V2,T2, then work done is W=μRT2-T11-γ, where γ=CPCV and R= universal gas constant.

Statement - II : In the above case, when work is done on the gas, the temperature of the gas would rise.

  1. Both statement-I and statement-II are true.
  2. Both statement-I and statement-II are false.
  3. Statement-I is true but statement-II is false.
  4. Statement-I is false but statement-II is true.

Solution

The work done in an adiabatic process is given by,

Wadiabatic =nRTf-Ti1-γ→ statement I is true.

For adiabatic process ∆Q=0. From the first law of thermodynamics,

∆Q=W+ΔU

0=W+ΔU

ΔU=-W

If work is done on the gas, i.e. work is negative

∴ΔU is positive.

∴ The temperature will increase. Hence, statement II is also true.

Asked in: JEE Main 2022 (28 Jun Shift 1)

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