Isothermal Process MCQ - Practice Questions with Answers

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, 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 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 a graph of the isothermal process - 

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

ii) Slope of isothermal curve : 

     By differentiating PV = C

$$
P d V+V d P=0 \Rightarrow P d V=-V d P \Rightarrow \frac{d P}{d V}=-\frac{P}{V}
$$

$$
\tan \theta=\frac{d P}{d V}=\frac{-P}{V}
$$

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

The formula of Work done in the isothermal process - 

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