Question

Quantity a of an ideal gas is at absolute temperature t, and a second quantity b of the same gas is at absolute temperature 2t. heat is added to each gas, and both gases are allowed to expand isothermally. part a if both gases undergo the same entropy change, is more heat added to gas a or gas b?

Answer 1

More heat is added to gas b compared to gas a because their absolute temperatures are different.

Step-by-step explanation:

In an isothermal expansion, the change in entropy of a gas is given by ΔS = Q/T, where ΔS is the entropy change, Q is the heat added to the gas, and T is the absolute temperature of the gas. Since both gases undergo the same entropy change, their entropy changes are equal, meaning that ΔSa = ΔSb. Substituting the equation for entropy change, we get Qa/Ta = Qb/Tb. Since Tb = 2Ta, we can rearrange the equation to get Qa/Qb = Ta/2Ta = 1/2. Therefore, more heat is added to gas b than gas a.