Question

When $Q$ amount of heat is supplied to an ideal monoatomic gas, the gas performs $\frac{Q}{2}$ amount of work on its surrounding, then the molar heat capacity for the process is

• A. $2R$
• B. $1.5R$
• C. $3R$
• D. $2.5R$

Answer 1

Answer: (C)

$Q=\Delta U+W$
$Q=\Delta U+\frac{Q}{2}$
$\Rightarrow \Delta U=\frac{Q}{2}$
$\Rightarrow $ $\Delta U=\frac{3}{2}nR\Delta T=\frac{Q}{2}$
$C=\frac{Q}{n \Delta T}$
$\Rightarrow C=3R$