An ideal gas sample ( γ = 1.5 ) is adiabatically compressed from a volume of 150 cm^3 to 50 cm^3 . The initial pressure and initial temperature are 150 kPa and 300 K . Determine the work done by the gas during this

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Correct answer: B. -33 J

Given P_1 = 150 kPa = 150 × 10^3 Pa , V_1 = 150 cm^3 = 150 × 10^ -6 m^3 , V_2 = 50 cm^3 = 50 × 10^ -6 m^3 , and γ = 1.5 . The work done by the gas in an adiabatic process is given by: W = (P_1 V_1 - P_2 V_2)/(γ - 1) Using the adiabatic relation P_1 V_1^γ = P_2 V_2^γ , we can rewrite P_2 V_2 as P_1 V_1 ((V_1)/(V_2))^ γ - 1 . Substituting this into the work equation: W = (P_1 V_1)/(γ - 1) [1 - ((V_1)/(V_2))^ γ - 1 ] Substituting the given values: W = 150 × 10^3 × 150 × 10^ -6 1.5 - 1 [1 - ((150)/(50))^ 1.5 - 1 ] W = (22.5)/(0.5) [ 1 - (3)^ 0.5 ] W = 45 (1 - 3 ) Using 3 1.732 : W = 45 (1 - 1.732) = 45 × (- 0.732) = -32.94 J Rounding to the nearest integer, W - 33 J.

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