N moles of an ideal gas undergoes a process

Asked by admin @ 13/08/2021 in Physics viewed by 308 People

N moles of an ideal gas undergoes adiabatic process and changes its state from P1,V1,T1 to P2,V2,T2 . The change in internal energy of the gas will be

Answered by admin @ 13/08/2021

The ideal gas undergoes adiabatic process, so no heat enters or leaves the system, i.e., $\tt{\Delta q=0.}$

By first law of thermodynamics,

$\tt{\longrightarrow \Delta u=\Delta q+\Delta W}$

or,

$\tt{\longrightarrow \Delta u=\Delta W\quad\quad[\because\,\Delta q=0]}$

I.e., the work done on the system is completely utilized by the system to change its internal energy.

Work done in an adiabatic process is,

$\tt{\longrightarrow \Delta W=\dfrac{P_1V_1-P_2V_2}{1-\gamma}}$

This is the same as the internal energy.

$\tt{\longrightarrow\underline{\underline{\Delta u=\dfrac{P_1V_1-P_2V_2}{1-\gamma}}}}$

In terms of temperature,

$\tt{\longrightarrow\underline{\underline{\Delta u=\dfrac{NR(T_1-T_2)}{1-\gamma}}}}$

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