Isochoric Process - Practice Questions & MCQ

Isochoric Process- A Thermodynamic process in which volume remains constant is known as the Isochoric Process.

In this process P and T changes keeping P constant. So Gay-Lussac’s law is obeyed in this process.

  Key points in the Isochoric Process 

•  Its Equation of state is given as $\frac{P}{T}=$ constant

  $\text{ or }\frac{P_1}{T_1}=\frac{P_2}{T_2}=\text{ constant }$

  - P-V Indicator diagram for an isobaric process

  Its PV graph has slope= infinity (i.e $\frac{dP}{dV}=\mathrm{\infty }$,

The above Graph represents an Isochoric increase in pressure at volume V.

 The P-V diagram for this process is a  line is parallel to the pressure line.

• Specific heat of gas during Isochoric process is given by

$C_V=\frac{f}{2}R$

- The bulk modulus of elasticity during Isochoric process is given by

$K=\frac{\mathrm{\Delta }P}{-\mathrm{\Delta }V/V}=\frac{\mathrm{\Delta }P}{0}=\mathrm{\infty }$

- Work done in Isochoric process-

$\begin{array}{rl}& \mathrm{\Delta }W=P\mathrm{\Delta }V\\ & \text{ and as }\mathrm{\Delta }V=0\\ & \text{ So }\mathrm{\Delta }W=0\end{array}$

- Internal energy in Isochoric process

$\mathrm{\Delta }U=n{C}_V\mathrm{\Delta }T=n\frac{R}{(\gamma -1)}\mathrm{\Delta }T$

- Heat in Isochoric process

From FLTD $\mathrm{\Delta }Q=\mathrm{\Delta }U+\mathrm{\Delta }W$
But $\mathrm{\Delta }W=0$

$\mathrm{\Delta }Q=\mathrm{\Delta }U=n{C}_V\mathrm{\Delta }T=n\frac{R}{(\gamma -1)}\mathrm{\Delta }T=\frac{P_f{V}_f-P_i{V}_i}{\gamma -1}$
 

• Examples of Isochoric process-

1. Heating of water in a pressure cooker (Valve closed)