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Q.

An ideal gas is heated at constant pressure. The work done by the gas is one-third of the heat supplied. Find the value of $γ = C_{P} / C_{v}$ :

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a

1.4

b

1.5

c

1.60

d

1.67

answer is B.

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Detailed Solution

$\begin{array}{l} C_{P} = \frac{R γ}{γ - 1}, d Q = n C_{P} d t, d U = n C_{v} d T \\ d W = d Q - d U = n (C_{P} - C_{v}) d T = n R d T \\ d Q = Q, n d T = \frac{Q}{C_{P}} \\ d W = n R d T = \frac{R Q}{C_{P}} = R Q \times \frac{γ - 1}{R γ} = \frac{Q}{3} (g i v e n) \\ \frac{γ - 1}{γ} = \frac{1}{3} \Rightarrow γ = 1.5 \end{array}$

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An ideal gas is heated at constant pressure. The work done by the gas is one-third of the heat supplied. Find the value of γ=CP/Cv :