A quantity of carbon monoxide gas is slowly compressed adiabatically in an insulated container to one-half of its initial volume.The ratio of the specific heat capacities at constant pressure and constant volume,cP/cV ,for carbon dioxide is approximately 1.3.Determine the final pressure of the gas if the initial pressure is 2.0 × 10⁵ Pa.

Question

Quizplus · Accepted Answer

For an adiabatic process, the relation between pressure and volume is given by $P_1V_1^\gamma = P_2V_2^\gamma$, where $\gamma = \frac{c_P}{c_V}$. Given $\gamma = 1.3$, $V_2 = \frac{1}{2}V_1$, and $P_1 = 2.0 \times 10^5$ Pa, we can solve for $P_2$. Substituting the values, we get $P_2 = P_1 \left(\frac{V_1}{V_2}\right)^\gamma = 2.0 \times 10^5 \times (2)^{1.3} \approx 4.9 \times 10^5$ Pa.

A Quantity of Carbon Monoxide Gas Is Slowly Compressed Adiabatically