Question

A mono atomic ideal gas undergoes a process in which the ratio of $P$ to $V$ at any instant is constant and equals to $1$, what is the molar heat capacity of the gas.

• A. $\frac{4R}{2}$
• B. $\frac{3R}{2}$
• C. $\frac{5R}{2}$
• D. $1.83R$

Answer 1

The correct option is A $\frac{4R}{2}$

$\begin{array}{c}{P}_1{V}_1=RT\\ C_V=\frac{3}{2}R\\ \frac{P}{V}=1\\ \therefore P=V\\ dq=C_{V}dT+pdV\\ For1moleofgasPV=Rt\\ Ondifferntiating,\\ pdV+VdP=RdT\\ \therefore 2pdV=RdT\\ pdV=\frac{RdT}{2}\\ \therefore dq=C_{v}dT+\frac{RdT}{2}\\ =\frac{3}{2}R+\frac{RdT}{2}\\ =\frac{4R}{2}\end{array}$