Question

a beaker of water comprises a thermodynamic system.The system undergoes a process in which the system gains 18 kJ of heat to the surroundings while the surrounding performs 24 kJ of work on the system. Calculate the change in internal energy of the system. You must show all work.

Answer 1

The change in internal energy of the system is calculated using the first law of thermodynamics. With 18 kJ of heat added to the system and 24 kJ of work performed on it, the internal energy decreases by 6 kJ.

Step-by-step explanation:

To calculate the change in internal energy of the thermodynamic system, the first law of thermodynamics is applied, which states that the change in internal energy (ΔU) of the system is equal to the heat added to the system (Q) minus the work done by the system (W): ΔU = Q - W.

In this problem:

• The system gains 18 kJ of heat. Therefore, Q = +18 kJ.
• The surrounding performs 24 kJ of work on the system, which means work is done on the system, not by it. Hence, W = +24 kJ. (Note: when work is done on the system, it's considered positive in this equation).

The change in internal energy can be found using the formula:

ΔU = Q - W
ΔU = 18 kJ - 24 kJ
ΔU = -6 kJ

The system has a decrease in internal energy of 6 kJ.