Question

In a thermodynamic system contained in a rigid vessel with a paddle wheel undergoing an adiabatic process, kinetic and potential energy changes are negligible. Which of the following equations is correct?

a. (Q = Δ U)

b. (Q = Δ U + W)

c. (Q = W)

d. (Q = Δ H)

Answer 1

The correct equation for an adiabatic process where no heat transfer occurs is (Q = Δ U + W), but Q = 0 and W is negative, making Δ U = -W.

Step-by-step explanation:

The correct equation for an adiabatic process in a rigid vessel with a paddle wheel, where kinetic and potential energy changes are negligible, is (Q = Δ U + W). However, for an adiabatic process, Q is equal to zero since there is no heat transfer into or out of the system. This fact, combined with the first law of thermodynamics which states Δ U = Q - W, implies that Δ U is actually equal to -W, where W is the work done by the system. Therefore, option (b) (Q = Δ U + W) is only correct if W is negative and equals to the negative of Δ U, signifying work done on the system.