How will the gas pressure change if it is isothermally compressed 5 times?

Given:

P is the initial gas pressure;

V is the initial gas volume;

V1 = V / 5 – the gas was compressed 5 times.

It is required to determine how the final gas pressure P1 / P2 will change.

According to the condition of the problem, the process took place at a constant temperature, that is, isothermal. Then:

P * V = P1 * V1;

P * V = P1 * V / 5;

P1 = P * V / (V / 5) = 5 * P * V / V = 5 * P.

I.e,

P1 / P = 5 * P / P = 5.

Answer: if you compress the gas 5 times, then the gas pressure will also increase 5 times.