Question

A monatomic 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. $\frac{4 R}{2}$
• B. $\frac{3 R}{2}$
• C. $\frac{5 R}{2}$
• D. $0$

Answer 1

Answer: (A)

A monoatomic ideal gas undergoes a process in which the ratio of $P$ to $V$ at any instant is constant and equals $1$ .
$\frac{P}{V}=$ constat
$P V^{-1}=$ constant
$P V^{\gamma}=$ constant
$\gamma=-1$
Monoatomic gas:
$C_{V}=\frac{3}{2} R$
Molar heat capacity $=C_{V}+\frac{R}{1-\gamma}$
$=\frac{3}{2} R+\frac{R}{1-(-1)} $
$=\frac{3}{2} R+\frac{R}{2}=\frac{4 R}{2}$