Question

Three moles of an ideal gas undergo a reversible isothermal compression at temperature 20.0 C. During this compression, an amount of work totalling 1900J is done on the gas.

What is the change of entropy of the gas?

Answer 1

In the reversible isothermal compression of an ideal gas, the change in entropy is zero because no heat is transferred to the system during this process.

Step-by-step explanation:

The question concerns the entropy change of an ideal gas during a reversible isothermal compression. In such a process, the temperature of the system remains constant, and the second law of thermodynamics states that the change in entropy (ΔS) is equal to the heat transferred (Q) divided by the temperature (T), where temperature is in Kelvin.

Since the compression is done on the gas, the work is negative indicating that work is done on the system (gas), and no heat transfer occurs to the system in an isothermal process of an ideal gas. This means the entropy of the system remains constant during an isothermal reversible compression. Therefore, despite 1900 J of work being done on the gas, the change in entropy, ΔS, is zero for the isothermal process.

It's important to note that if heat were transferred, we could calculate the change in entropy using the formula ΔS = Q/T. However, in the absence of heat transfer in a reversible isothermal process for an ideal gas, the entropy remains constant.