Isothermal Process - Practice Questions & MCQ

Isothermal process - When a thermodynamic system undergoes a thermodynamic process in such a way that its temperature remains constant, then that process is called an Isothermal process.

So, $\mathrm{T}=$ constant and $\Delta T=0$.

Trick to recognize isothermal process -
- The walls of the container must be perfectly conducting (no resistance) which allows the exchange of heat between the gas and surroundings.
- The process of compression or expansion should be infinitely slow so that the process gets proper time for the exchange of heat.

Equation of isothermal process -
As we know that the equation of state is given by $-P V=n R T$
If $\mathrm{T}=$ constant and for a particular amount of gas ' $n$ ' is also constant.
So we can write that - P.V $=$ Constant

Points in graph of isothermal process - 

i) Curves obtained on P-V graph are called isotherms and the graphs are hyperbolic in nature.

ii) Slope of isothermal curve : 

     By differentiating PV = C

$$
\begin{gathered}
P d V+V d P=0 \Rightarrow P d V=-V d P \Rightarrow \frac{d P}{d V}=-\frac{P}{V} \\
\tan \theta=\frac{d P}{d V}=\frac{-P}{V}
\end{gathered}
$$

iii) The area between the isothermal curve and volume axis represents the work done in the isothermal process.

The formula of Work done in the isothermal process -

$$
\begin{aligned}
& W=n R T \log _e\left(\frac{V_f}{V_i}\right)=2.303 n R T \log _{10}\left(\frac{V_f}{V_i}\right) \\
& W=n R T \log _e\left(\frac{P_i}{P_f}\right)=2.303 n R T \log _{10}\left(\frac{P}{P_f}\right)
\end{aligned}
$$