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

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 that 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 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

$$\begin{array}{c}PdV+VdP=0\Rightarrow PdV=-VdP\Rightarrow \frac{dP}{dV}=-\frac{P}{V}\\ \tan \theta =\frac{dP}{dV}=\frac{-P}{V}\end{array}$$

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 -

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