A chamber of gas undergoes an adiabatic compression such that the final volume is reduced to half of its original value. The final pressure (compared to the original pressure) is

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During an adiabatic compression, the work done on the gas increases its internal energy, which in turn increases its temperature and pressure. The relationship between pressure and volume in an adiabatic process for an ideal gas is given by $P_1V_1^\gamma = P_2V_2^\gamma$, where $\gamma$ (gamma) is the heat capacity ratio (Cp/Cv) and is always greater than 1. Since the volume is halved ($V_2 = \frac{1}{2}V_1$), and $\gamma > 1$, the final pressure $P_2$ is more than doubled compared to the initial pressure $P_1$.

A Chamber of Gas Undergoes an Adiabatic Compression Such That