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 . Calculate the final pressure and final temperature

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Correct answer: A. 780 kPa , 520 K

For an adiabatic process, the relation between pressure and volume is given by

P_1 V_1^\gamma = P_2 V_2^\gamma

.

Substituting the given values:

P_2 = P_1 \left(\dfrac{V_1}{V_2}\right)^\gamma

P_2 = 150 \times \left(\dfrac{150}{50}\right)^{1.5}

P_2 = 150 \times 3^{1.5} = 150 \times 3\sqrt{3} = 450 \times 1.732 \approx 780 \text{ kPa}

The relation between temperature and volume for an adiabatic process is

T_1 V_1^{\gamma - 1} = T_2 V_2^{\gamma - 1}

.

T_2 = T_1 \left(\dfrac{V_1}{V_2}\right)^{\gamma - 1}

T_2 = 300 \times \left(\dfrac{150}{50}\right)^{1.5 - 1}

T_2 = 300 \times 3^{0.5} = 300\sqrt{3} = 300 \times 1.732 \approx 520 \text{ K}

An ideal gas sample ( γ = 1.5 ) is adiabatically compressed from a...

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