The cylindrical vessel is filled with gas at a temperature of 27 degrees C and a pressure of 100 kPa and

The cylindrical vessel is filled with gas at a temperature of 27 degrees C and a pressure of 100 kPa and is divided in half by a movable partition. What will be the pressure if the gas in one half is heated to a temperature of 57 degrees C, and in the second half the gas temperature is left unchanged?

Ideal gas equation of state: P * V = m * R * T / M;
So for both parts of the vessel, you can write: P1 * V1 = k * T1;
1 * 10 ^ 5 Pa * V1 = k * (27 + 273) K;
1 * 10 ^ 5 Pa * V1 = k * 300 K (1);
After heating in the first part:
P2 * V2 = k * T2;
P2 * V2 = k * 330 K (2);
In the second half after heating:
P2 * V3 = k * 300 K (3);
And finally, since the volume of the vessel has not changed entirely, one more equation can be written:
2 * V1 = V2 + V3 (4);
From (1) we express V1, from (2) we express V2, from (3) we express V3 and substitute all this in (4):
2 * 300 * k / 1 * 10 ^ 5 = 330 * k / P2 + 300 * k / P2 (5);
We divide both sides of (5) by k:
2 * 300/10 ^ 5 = 330 / P2 + 300 / P2;
600/10 ^ 5 = 630 / P2;
P2 = 10 ^ 5 * 630/600 = 1.05 * 10 ^ 5 = 105 kPa;
Answer: 105 kPa