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Thermodynamics — Physics STD 11 Science — Question

Gujarat 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. $C_p$ and $C_v$.
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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 $C_V$ 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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