Question

When 1 mol gas is heated at constant volume, temperature is raised from 298 to 308 K. Heat supplied to the gas is 500 J. Then which statement is correct:

a) ΔU = 500 J
b) ΔQ = 500 J
c) ΔW = 500 J
d) ΔH = 500 J

Answer 1

The correct statement is a) ∆U = 500 J because no work is done as the volume remains constant, and the heat added to the gas represents the change in its internal energy.

Step-by-step explanation:

When 1 mol of gas is heated at constant volume, and its temperature is raised from 298 K to 308 K with 500 J of heat supplied to the gas, we must determine which statement is correct. In this process, no work is done on or by the gas since the volume remains constant. According to the first law of thermodynamics, which states that the change in internal energy (∆U) is equal to the heat added to the system (∆Q) minus the work done by the system (∆W), we have ∆U = ∆Q - ∆W. Since the volume is constant and ∆W = 0, the answer is a) ∆U = 500 J. The amount of heat added is indeed the change in internal energy of the gas since no work is done during this process.