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For a gas, the difference between the two specific heats is $5000 J {kg}^{- 1} K^{- 1}$ . The ratio of specific heats is 1.6. The specific heat at constant pressure is

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13333 .3 J {kg}^{- 1} K^{- 1}

1333 .33 J {kg}^{- 1} K^{- 1}

1333333 .3 J {kg}^{- 1} K^{- 1}

133333 .0 J {kg}^{- 1} K^{- 1}

answer is B.

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Detailed Solution

given that

$C_{p} - C_{v} = 5000 {Jkg}^{- 1} k^{- 1}$

$\frac{C_{p}}{C_{v}} = 1.6$

$C_{p} = ?$

$C_{p} = 1.6 C_{v}$

$\Rightarrow 1.6 C_{v} - C_{v} = 5000$

$\Rightarrow C_{v} = \frac{5000}{0.6}$

$\Rightarrow C_{p} = 1.6 \times \frac{5000}{0.6} = \frac{8000}{6}$

$= 1.3333 \times 10^{4}$

$\Rightarrow C_{p} = 13333.3 {Jkg}^{- 1} k^{- 1}$

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