First slide

Heat given

Question

The volume of 1 kg of hydrogen gas at N.T.P is 11.2 m³. Specific heat of hydrogen at constant volume is 10046J kg^–1K^–1. Find the specific heat at constant pressure in Jkg^-1k^-1.

Moderate

A

12020
B

14220
C

16340
D

18230

Solution

m = 1kg ; v = 11.2m³;
$\rho = 1atm = 1.01 \times {10^5}Pa$
T = 273 K
${C_P} = 10046JK{g^{ - 1}}{k^{ - 1}}$
C_p = ?
PV = mrT
$\therefore r = \frac{{PV}}{{mT}} = \frac{{1.01 \times {{10}^5} \times 11.2}}{{1 \times 273}}J/Kg - K$
= 14220 J/kg - K
$Cp - {C_v} = r;{C_p} = r + {C_v}$
${C_p} = 10046 + 4143.59 = 14189 \approx 14220Jk{g^{ - 1}}{k^{ - 1}}$

$\Rightarrow r = 4143.59\,\,J/kg - K$
$\therefore {C_p} = \left( {4143.59 + 10046} \right)\,\,J/kg - K$

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