With isochoric heating, the gas temperature increased 5 times. what was the initial pressure in the vessel

With isochoric heating, the gas temperature increased 5 times. what was the initial pressure in the vessel if at the end it turned out to be equal to 5 MPa.

Given:

T2 = 5 * T1 – the gas temperature has increased 5 times;

P2 = 5 MPa = 5 * 106 Pascal.

It is required to determine P1 (Pascal) – the initial gas pressure.

Since, according to the condition of the problem, the process occurs at a constant volume (isochore, V = const), in order to determine the initial gas pressure, it is necessary to use the following equality:

P1 / T1 = P2 / T2;

P1 = P2 * T1 / T2;

P1 = P2 * T1 / (5 * T1);

P1 = P2 / 5 = 5 * 106/5 = 1 * 106 Pascal = 1 MPa.

Answer: the initial gas pressure is 1 MPa.