Question

An ideal gas undergoes an isothermal expansion. What will happen to its entropy? a) It will increase. c) It's impossible to determine. b) It will decrease. d) It will remain unchanged.

Short answer

Answer: a) It will increase.

Step-by-step solution

Understand the isothermal process in an ideal gas

An isothermal process is a thermodynamic process in which the temperature of the system remains constant. In the case of an ideal gas, when it undergoes an isothermal expansion, pressure (P) and volume (V) change in such a way that the product of pressure and volume (PV) remains constant.

Recall the mathematical expression for entropy change

The entropy change (∆S) of an ideal gas in an isothermal process can be expressed as: ∆S = nR * ln(V2/V1) where n is the number of moles of the gas, R is the universal gas constant, V1 and V2 are the initial and final volumes of the gas, and ln represents the natural logarithm.

Analyze the effect of isothermal expansion on entropy

Since the process is an expansion, the final volume (V2) will be greater than the initial volume (V1). In the entropy change equation, the ratio V2/V1 will be greater than 1. As the natural logarithm of a number greater than 1 is positive, the entropy change ∆S will be positive.

Choose the correct answer

As we found that the entropy change (∆S) is positive, it implies that the entropy of the ideal gas will increase during an isothermal expansion. So, the correct answer is: a) It will increase.