Why Might Statement (b) Be Incorrect in Ideal Gas Processes?

[grangr]

Homework Statement

Which of the following statement(s) is (are) correct when an ideal gas goes from an initial to a final state in a single process?

a. No work is done on or by the gas when the volume remains constant.
b. No energy is transferred into or out of the gas as heat transfer when the temperature remains constant.
c. The internal energy of the gas does not change when the pressure remains constant.
d. All the statements above are correct.
e. Only statements (a) and (b) above are correct.​

Homework Equations

• ΔH = ΔE + Δ(PV) = Q + W + Δ(PV), and for ideal gas, ΔH = nC_vΔT + Δ(nRT) = nC_vΔT + nRΔT = nC_pΔT

The Attempt at a Solution

The answer given is (a), while my attempt was (e). I do not understand why (b) is incorrect.

a. Given constant V, ΔV = 0, thus W = 0. (a) is correct.
b. Given constant T on ideal gas, ΔE (or ΔU, internal energy) = 0, thus there is no energy transferred as heat in or out of the system. But why is (b) incorrect then?
c. Given constant P, ΔP = 0, therefore W = - PΔV. Thus ΔH = Q - PΔV + P(ΔV) = Q_p. As there might be heat exchange, (c) may or may not hold.

Thank you for your help.

 

[mjc123]

In b), if the volume changes, there is PV work done, and if the temperature is maintained constant, heat must be supplied or released to balance this work.

 

[grangr]

In b), if the volume changes, there is PV work done, and if the temperature is maintained constant, heat must be supplied or released to balance this work.

Thank you for your reply. I see. So in (b), it could be like an isothermal process, where ΔT = 0 (thus ΔE = 0) but Q ≠ 0.