The air in the cylinder under the piston was first isothermally compressed by increasing the pressure

The air in the cylinder under the piston was first isothermally compressed by increasing the pressure by a factor of 2, and then heated at constant pressure. as a result, the volume has increased 3 times compared to the initial one. to what temperature the gas was heated if the initial temperature was 300K.

Given:

T = 300 Kelvin – the initial temperature of the air in the cylinder;

P1 = 2 * P – in the isothermal process, the pressure was doubled;

V2 = 3 * V – at constant pressure, the volume has increased 3 times.

It is required to determine the final air temperature T1 (Kelvin).

Let the initial gas volume be V, and the pressure P. Then, in the first process (isothermal):

P * V = P1 * V1;

P * V = 2 * P * V1;

V1 = V / 2.

In the second process (at constant pressure):

V1 / T = V2 / T1;

V / (2 * T) = 3 * V / T1;

1 / (2 * T) = 3 / T1;

T1 = 3 * 2 * T = 6 * T = 6 * 300 = 1800 Kelvin.

Answer: the gas was heated to a temperature of 1800 Kelvin.