With a constant mass of gas, a process takes place in which the pressure is always proportional to the volume.

With a constant mass of gas, a process takes place in which the pressure is always proportional to the volume. It is known that the initial gas pressure is 1 * 10 ^ 5 Pa, the initial temperature is 327 C, the final pressure is 5 * 10 ^ 4 Pa. Determine its final temperature.

According to the Mendeleev – Clapeyron equation, where m is const: p0 * v0 / t0 = p * v / t

By condition, the pressure is proportional to the volume, which means p0 / p = v0 / v = 1 * 10 ^ 5 Pa / 5 * 10 ^ 4 Pa = 2, p / p0 = v / v0 = 1/2

We express t from the equation: t = p * v * t0 / (p0 * v0) = 1/2 * 1/2 * 327 ° C = 81.75 ° C