SATHEE: Kinetic Theory - Result Question 37

Kinetic Theory - Result Question 37

37. For a certain gas the ratio of specific heats is given to be $γ = 1.5$ . For this gas

(a) $C_{V} = 3 R / J$

(b) $C_{P} = 3 R / J$

(c) $C_{P} = 5 R / J$

(d) $C_{V} = 5 R / J$

[1990]

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Answer:

Correct Answer: 37. (b)

Solution:

(b) $γ = \frac{C_{P}}{C_{V}} = \frac{15}{10} = \frac{3}{2} \Rightarrow C_{V} = \frac{2}{3} C_{P}$

$C_{P} - C_{V} = \frac{R}{J} \Rightarrow C_{P} - \frac{2}{3} C_{P} = \frac{R}{J}$

$\Rightarrow \frac{C_{P}}{3} = \frac{R}{J} \Rightarrow C_{P} = \frac{3 R}{J}$

38 .

(d) $C_{p} = \frac{5}{2} R$ and $C_{v} = \frac{3}{2} R$

We know that $Q_{v} = n C_{v} Δ T$ and $Q_{p} = n C_{p} Δ T$

$\Rightarrow \frac{Q_{v}}{Q_{p}} = \frac{3}{5}$ .

Given $Q_{p} = 207 J \Rightarrow Q_{v} ≅ 124 J$

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