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 $\mathrm{\Delta }T=0$.

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 $-PV=nRT$
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

$$PdV+VdP=0\Rightarrow PdV=-VdP\Rightarrow \frac{dP}{dV}=-\frac{P}{V}$$

$$\tan \theta =\frac{dP}{dV}=\frac{-P}{V}$$

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 - 

$\begin{array}{rl}& W=nRT{\log }_e\left(\frac{V_f}{V_i}\right)=2.303nRT{\log }_{10}\left(\frac{V_f}{V_i}\right)\\ & W=nRT{\log }_e\left(\frac{P_i}{P_f}\right)=2.303nRT{\log }_{10}\left(\frac{P_i}{P_f}\right)\end{array}$