A cylinder containing an ideal gas has a volume of 2 m³ and a pressure of 1.7 × 10⁵ Pa at a temperature of 400 K.The cylinder is placed against a metal block that is maintained at 900 K and the gas expands as the pressure remains constant until the temperature of the gas reaches 900 K.The change in internal energy of the gas is +6.5 × 10⁵ J.How much heat did the gas absorb?

Question

Quizplus · Accepted Answer

The heat absorbed by the gas is equal to the change in internal energy plus the work done by the gas. Since the pressure is constant, work done (W) is PΔV. The volume change (ΔV) can be calculated using the ideal gas law: V2/V1 = T2/T1, giving V2 = 4.5 m³. Thus, ΔV = 2.5 m³. Work done W = PΔV = 1.7 × 10⁵ Pa × 2.5 m³ = 4.25 × 10⁵ J. Therefore, heat absorbed Q = ΔU + W = 6.5 × 10⁵ J + 4.25 × 10⁵ J = 10.75 × 10⁵ J, approximately 10.8 × 10⁵ J.

A Cylinder Containing an Ideal Gas Has a Volume of 2