Heat - 4

Classical Mechanics Level 4

One mole of an ideal gas undergoes a process P = P o 1 + ( V o / V ) 2 P = \dfrac{P_{o}}{1 + (V_{o}/V)^2} where P o , V o P_{o},V_{o} are constants. The change in temperature of the gas when volume is changed from V = V o V = V_{o} to V = 2 V o V = 2V_{o} is a P o V o R a\dfrac{P_{o}V_{o}}{R} where R R is universal gas constant.

Find the value of a a .

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The answer is 1.1.

Ram Mohith by Ram Mohith , 18, India

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1 solution

Using the equation of state of an ideal gas, P V = μ R T PV=\mu RT , (here μ = 1 \mu =1 mole) we get T = P 0 V 3 R ( V 2 + V 0 2 ) T=\dfrac{P_0V^3}{R(V^2+V_0^2)} . Using the given data we get the change in temperature equal to ( 8 5 − 1 2 ) P 0 V 0 R = 11 10 P 0 V 0 R (\dfrac{8}{5}-\dfrac{1}{2})\dfrac{P_0V_0}{R}=\dfrac{11}{10}\dfrac{P_0V_0}{R} . Hence a = 11 10 = 1.1 a=\dfrac{11}{10}=\boxed {1.1}

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