Question

The specific heat of hydrogen gas at constant pressure is $C_{p}=3.4 \times 10^{3} cal / kg ^{\circ} C$ and at constant volume is $C_{V}=2.4 \times 10^{3} cal / kg ^{\circ} C$. If one kilogram hydrogen gas is heated from $10^{\circ} C$ to $20^{\circ} C$ at constant pressure, the exterted work done on the gas to maintain it at constant pressure is

• A. $10^{5} cal$
• B. $10^{4} cal$
• C. $10^{3}$ cal
• D. $5 \times 10^{3} cal$

Answer 1

Answer: (B)

From first law of thermodynamics, $\Delta Q=\Delta U+W$
Work done at constant pressure
$(\Delta W)_{p}=(\Delta Q)_{p}-\Delta U$
$=(\Delta Q)_{p}-(\Delta Q)_{V}\left(A s\right.$,
we know $\left.\Delta Q_{V}=\Delta U\right)$
Also $(\Delta Q)_{p}=M C_{p} \Delta T$
and $(\Delta Q)_{V}=M C_{V} \Delta T$
$\Rightarrow \left(\Delta W_{p}\right)=M\left(C_{p}-C_{V}\right) \Delta T$
$ =1 \times\left(3.4 \times 10^{3}-2.4 \times 10^{3}\right) \times 10$
$=10^{4}\, cal$