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

a) It will increase b) It will decrease c) No change d) It's impossible to determine Answer: a) It will increase.

Step-by-step solution

Recall the formula for entropy change.

For an ideal gas undergoing an isothermal process, the entropy change can be calculated using the formula: ΔS = n * R * ln(V2/V1) where ΔS is the change in entropy, n is the number of moles of gas, R is the ideal gas constant, V1 is the initial volume, and V2 is the final volume.

Determine if the volume increases or decreases.

Since the gas is undergoing an expansion, the final volume (V2) must be larger than the initial volume (V1). In other words, V2 > V1.

Calculate the logarithm term.

Since V2 > V1, the ratio (V2/V1) will be greater than 1. Therefore, ln(V2/V1) will be greater than 0.

Calculate the entropy change.

As ΔS = n * R * ln(V2/V1), and ln(V2/V1) is greater than 0, so ΔS will also be greater than 0. This means that the change in entropy is positive.

Determine the correct answer.

Since we found the change in entropy to be positive, there is an increase in the entropy of the gas. Therefore, the correct answer is: a) It will increase.