The gas is heated from 300 to 450 K at constant pressure, while the volume increases by 2 liters.

The gas is heated from 300 to 450 K at constant pressure, while the volume increases by 2 liters. Determine the final gas volume.

Given: T1 = 450 K;

T2 = 300 K;

dv = 2 liters;

Find: v2 -?

Solution:

The pressure is constant (p = const), according to the Gay-Lussac law (isobaric process):
v1 / T1 = v2 / T2, by condition we have v2 = v1 + dv (dv = 2 liters).

Substitute in the formula:
v1 / T1 = (v1 + dv) / T2;

Now let’s solve this equation for v1.
v1 * T2 = (v1 + dv) * T1.
v1 * T2 = v1 * T1 + dv * T1.
v1 * T2 – v1 * T1 = dv * T1.
v1 * (T2 – T1) = dv * T1.
v1 = (dv * T1) / (T2 – T1).
v1 = (2 * 300) / (450 – 300) = 4 liters;
Find the final volume:
v2 = v1 + dv.
v2 = 4 + 2 = 6 liters.

Answer: 6 liters.