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Thermodynamics — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsThermodynamics5 Marks
Question
The difference between the two specific heat capacities (at constant pressure and volume) of a gas is 5000J kg-1 k-1 and the ratio of these specific heat capacities is 1.6. Find the two specific heat capacities i.e. Cp and Cv.
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Answer

We Know that,
$\text{C}_\text{P}-\text{C}_\text{V}=\text{R}$
$\text{C}_\text{P}-\text{C}_\text{V}=5000$
Dividing by CV we get,
$\frac{\text{C}_\text{P}}{\text{C}_\text{V}}-1=\frac{5000}{\text{C}_\text{V}}$
$1.6-1=\frac{5000}{\text{C}_\text{V}}$
$0.6=\frac{5000}{\text{C}_\text{V}}$
$\therefore\text{C}_\text{V}=\frac{5000}{\text{0.6}}$
$=8333.33\text{J/}\ \text{Kg}^{-1}\text{K}^{-1}$
Now, $\text{C}_\text{P}-\text{C}_\text{V}=5000$
$\text{C}_\text{P}-8333.33+5000$
$=13333.33\ \text{J}\ \text{Kg}^{-1}\text{K}^{-1}$

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