Question

A monoatomic ideal gas undergoes a process in which the ratio of $P$ to $V$ at any instant is constant and equal to unity. The molar heat capacity of gas is:

• A. $1.5R$
• B. $2.0R$
• C. $2.5R$
• D. $0$

Answer 1

The correct option is B $2.0R$

A monoatomic ideal gas undergoes a process in which the ratio of P to V at any instant is constant and equals 1.

$\frac{P}{V}=$ constant

$P{V}^{-1}=$ constant

$P{V}^{\gamma }=$ constant

$\gamma =-1$

Monatomic gas:

$C_V=\frac{3}{2}R$

Molar heat capacity $=C_V+\frac{R}{1-\gamma }$

$=\frac{3}{2}R+\frac{R}{1-(-1)}$

$=\frac{3}{2}R+\frac{R}{2}=\frac{4R}{2}=2R$