Question

Helium gas at 27 ºC and pressure of 1.6 atm is compressed adiabatically to one fourth of its original volume. Find the final pressure (in atm) of the gas. (2sgf)
γ=1.4

Answer 1

Adiabatic process can be represented by the polytropic process equation:

$$p_1V_1^{\gamma} =p_2V_2^{\gamma}$$

where $p_1 = 1.6 \space atm$ is the initial pressure, $p_2$ is the final pressure and $V_1, V_2$ are intial and final volumes respectively. They are related to each other in the following way, since the gas was compressed to one fourth of its original volume:

$$\dfrac{V_1}{V_2 } = 4$$

Expressing the final temperature, obtain:

$$p_2 = p_1 \left( \dfrac{V_1}{V_2} \right)^{\gamma} = 1.6\cdot 4 ^{1.4} \approx 11.14 \space atm$$

Answer. 11.14 atm.