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.

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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.

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12020

14220

16340

18230

answer is B.

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Detailed Solution

$\begin{array}{l} m = 1 kg; v = 11 .2 m^{3}; \\ ρ = 1 atm = 1 .01 \times 10^{5} Pa; T = 273 K \\ Cv = 10046 {JKg}^{- 1} k^{- 1}; Cp = ? \\ Cp - C_{v} = r; C_{p} = r + C_{v} \\ PV = mRT \\ r = \frac{PV}{MT} = \frac{1 .01 \times 10^{5} \times 11 .2}{1 \times 273} = 4143 .59 \\ C_{p} = 10046 + 4143 .59 = 14189 \approx 14220 {Jkg}^{- 1} k^{- 1} \end{array}$