In a vessel with a movable piston there is a gas of a certain mass. The gas was heated and its temperature

In a vessel with a movable piston there is a gas of a certain mass. The gas was heated and its temperature increased from 27 to 177 ° C. At the same time, the gas was compressed to half the volume. Assuming that the gas is ideal, determine how many times the gas pressure has changed.

According to Clapeyron’s gas law:

P1 * V1 / T1 = P2 * V2 / T2;

The temperature in this ratio is indicated in Kelvin.

From this equation, we express the ratio of gas pressures under conditions 1 and 2.

P2 / P1 = (T2 * V1) / (T1 * V2);

Considering that:

V1 = 2V2;

T1 = 273 + 27 = 300 K;

T2 = 273 + 177 = 450 K;

find the pressure ratio:

P2 / P1 = (450 * 2 * V2) / (300 * V2) = 3

Answer: the pressure will triple.