Question

\( \delta Q \) and \( \delta W \) are the heat and work interactions of a system with its surroundings, and \( dU \) is the change in the internal energy of the system. For an adiabatic process in a closed, constant pressure combustor, which one of the following options is correct?

• A. \( | \delta Q | = | dU | \neq 0 \) and \( | \delta W | = 0 \)
• B. \( | \delta Q | = | \delta W | = 0 \) and \( | dU | \neq 0 \)
• C. \( | \delta Q | = | \delta W | = | dU | = 0 \)
• D. \( | \delta W | = | dU | \neq 0 \) and \( | \delta Q | = 0 \)

Hint:

In adiabatic processes, the heat exchange with the surroundings is zero (\( \delta Q = 0 \)), and the change in internal energy is directly related to the work done by or on the system.

Answer 1

The Correct Option is D

In thermodynamics, the first law of thermodynamics is given by: \[ dU = \delta Q - \delta W \] Where:
\( dU \) is the change in internal energy,
\( \delta Q \) is the heat added to the system,
\( \delta W \) is the work done by the system.
For an adiabatic process, there is no heat exchange with the surroundings. Therefore: \[ \delta Q = 0 \] Now, substituting this into the first law of thermodynamics: \[ dU = 0 - \delta W \] \[ dU = - \delta W \] This means that the change in internal energy is equal to the negative of the work done by the system. So, both the change in internal energy and work are non-zero, while there is no heat exchange. Therefore, the correct answer is: \[ \boxed{(D) | \delta W | = | dU | \neq 0 { and } | \delta Q | = 0} \]