One mole of a monoatomic gas is enclosed in a cylinder and occupies a volume of 4 liter at a pressure 100 ~N / m ^2 . It is subjected to a process T = V ^2 , where is a positive constant, V is volume of the gas and T is Kelvin temperature.

Question

One mole of a monoatomic gas is enclosed in a cylinder and occupies a volume of 4 liter at a pressure 100 ~N / m ^2 . It is subjected to a process T = V ^2 , where is a positive constant, V is volume of the gas and T is Kelvin temperature. Find the work-done by gas (in joule) in increasing the volume of gas to six times initial volume.

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Correct answer: 7

w= P d V ; P= n R T V ; P= n R V n R _ V₀ ^ 6 V₀ V d v= n R 2 [ (6 V₀ )^2- (V₀ )^2 ]w= h R 2 (35) V₀^2= P₀ V₀ 35 2 ; ( = P₀ n R V₀ )

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