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Q.

A sample of ideal gas of some mass is taken through the cyclic process as shown in the figure.

The temperature of the gas at state A is T_A = 200K,and at state C is T_C =1800K .Choose the CORRECT option(s):

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a

V_A/V_C = 1/3

b

P_AV_A/P_CV_C = 1/3

c

V_A/V_C = 1/9

d

P_AV_A/P_CV_C = 1/9

answer is A, D.

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Detailed Solution

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$\begin{array}{l} \frac{V_{1}}{V_{3}} = \frac{1}{x} : P_{1} V_{1} T_{1} = P_{3} V_{3} T_{3} = {xP}_{1} {xV}_{1} T_{3} \\ T_{3} = \frac{T_{1}}{x^{2}} \\ x^{2} = \frac{T_{1}}{T_{3}} = \frac{200}{1800} = \frac{1}{9} \\ x = \frac{1}{3} \\ ∴ \frac{V_{3}}{V_{1}} = x = \frac{1}{3} \end{array}$

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A sample of ideal gas of some mass is taken through the cyclic process as shown in the figure.The temperature of the gas at state A is TA = 200K,and at state C is TC =1800K .Choose the CORRECT option(s):