By what percentage will the gas pressure in the vessel increase if the temperature rises by 40%?

By what percentage will the gas pressure in the vessel increase if the temperature rises by 40%? Consider the gas volume constant.

Given:

V1 = V2 – gas volume does not change;

n1 = 40% = 0.4 is the amount by which the gas temperature has increased.

It is required to determine n2 (%) – by what percentage the gas pressure will increase.

Let T1 and P1 be the initial gas temperature and pressure.

Then, after heating, the temperature will become equal to:

T2 = T1 + n1 * T1 = T1 * (1 + n1).

Since, according to the condition of the problem, the volume of gas does not change, then:

P1 / T1 = P2 / T2;

P2 = P1 * T2 / T1 = P1 * T1 * (1 + n1) / T1 = P1 * (1 + n1).

Then:

n2 = P2 / P1 = P1 * (1 + n1) / P1 = 1 + n1 = 1 + 0.4 = 1.4 or 140%.

That is, the gas pressure will also increase by 40.

Answer: if the gas temperature rises by 40%, the pressure will also increase by 40%.