A gas is confined in a cylindrical can fitted with a piston. Both the piston and the walls of the can are adiabatic. The initial pressure, volume, and temperature of the gas are 100 kPa , 400 cm^3 , and 300 K

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Correct answer: A. 800 kPa and 600 K

For a slow adiabatic compression, the process is reversible and follows the equation

P V^{\gamma} = \text{constant}

.

Given:

P_1 = 100 \text{ kPa}

V_1 = 400 \text{ cm}^3

T_1 = 300 \text{ K}

\gamma = 1.5

V_2 = 100 \text{ cm}^3

Using the pressure-volume relation:

P_1 V_1^{\gamma} = P_2 V_2^{\gamma}

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

P_2 = 100 \left( \dfrac{400}{100} \right)^{1.5}

P_2 = 100 \times 4^{1.5} = 100 \times 8 = 800 \text{ kPa}

Using the temperature-volume relation:

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 \left( \dfrac{400}{100} \right)^{1.5 - 1}

T_2 = 300 \times 4^{0.5} = 300 \times 2 = 600 \text{ K}

A gas is confined in a cylindrical can fitted with a piston. Both...

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