Question

The specific heat of hydrogen gas at constant pressure is $C_p=3.4\times 10^{3}cal/k{g}^{\circ }C$ and at constant volume is $C_V=2.4\times 10^{3}cal/k{g}^{\circ }C$. 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
$(\Delta W{)}_p=(\Delta Q{)}_p-\Delta U$
$=(\Delta Q{)}_p-(\Delta Q{)}_V(As$,
we know $\Delta Q_V=\Delta U)$
Also $(\Delta Q{)}_p=M{C}_p\Delta T$
and $(\Delta Q{)}_V=M{C}_V\Delta T$
$\Rightarrow \left(\Delta W_p\right)=M\left(C_p-C_V\right)\Delta T$
$=1\times \left(3.4\times 10^3-2.4\times 10^3\right)\times 10$
$=10^{4}cal$