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 $C_r=2.4\times {10}^{3}cal/k{g}^{\circ }C$ If one kilogram hydrogen gas is heated from ${10}^{\circ }$ to ${20}^{\circ }$ at constant pressure, the external work done on the gas to maintain it at constant pressure is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

From FLOT $△Q=△U+△W$
Work done at constant pressure $(△W{)}_P=(△Q{)}_P-△U$
$\left(△Q\right)-\left(△Q_V\right)$ ( As we know $(△Q{)}_V=△U$)
Also $(△Q{)}_P=m{c}_p△T$ and $(△Q{)}_V=m{c}_V△T$
$\Rightarrow (△W{)}_p=m(C_P-C_V)△T$
$\Rightarrow (△W{)}_P=1\times (3.4\times {10}^3-2.4\times {10}^3)\times 10={10}^{4}cal$