When the gas, the volume of which remains unchanged, was heated at T = 30

When the gas, the volume of which remains unchanged, was heated at T = 30, its pressure increased by 10%. What is the initial gas temperature?

Data: V (gas volume) = const; ΔT = 30 K; Pkg / Png (pressure increase) = 1.1 (10%).

To find out the initial temperature of the gas presented, consider the equality (isochoric process): Pkg / Tkg = Pkg / (Tng + ΔT) = Png / Tng, from where we express: Pkg / Png = (Tng + ΔT) / Tng = 1 + ΔT / Tng and Tng = ΔT / (Rkg / Rng – 1).

Let’s perform the calculation: Tng = ΔT / (Pkg / Rng – 1) = 30 / (1.1 – 1) = 300 K.

Answer: The initial temperature of the supplied gas was 300 K.