Question

600 J of heat is added to a monoatomic gas in a process in which the gas performs a work of 150 J. The molar heat capacity for the process is

• A. 3R
• B. 4R
• C. 2R
• D. 6R

Answer 1

Answer: (C)

2R

The first law of thermodynamics gives us the relation:
$q=\Delta U+w$
Given that
$q=600J$
$w=150J$
i.e. $\Delta U=450J$
$\Delta U=n{C}_v\Delta T=450J$
$q=nC\Delta T=600J$
$\frac{q}{\Delta U}=\frac{4}{3}$
$\frac{C}{C_v}=\frac{4}{3}$
$C=C_v\frac{4}{3}=\frac{3}{2}R\times \frac{4}{3}=2R$
Hence option C is correct.