Question

A vertical piston-cylinder device contains water and is being heated on top of a range. During the process, 65 Btu of heat is transferred to the water, and heat losses from the side walls amount to 8 Btu. The piston rises as a result of evaporation, and 5 Btu of work is done by the vapor. Determine the change in the energy of the water for this process.

Short answer

Question: Determine the change in energy of the water during the process in which heat is transferred, heat is lost from the side walls, and work is done by the vapor. Answer: The change in energy of the water during this process is 52 Btu.

Step-by-step solution

List the Given Information

We are given the following information: 1. Heat transferred to water: 65 Btu 2. Heat lost from side walls: 8 Btu 3. Work done by vapor: 5 Btu

Apply the First Law of Thermodynamics

The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W): ΔU = Q - W

Account for the Heat Loss from Side Walls

Since heat is lost through the side walls, the net heat added to the water will be the heat transferred to the water minus the heat losses from the side walls: Net heat added (Q_net) = Heat transferred to water - Heat lost from side walls Q_net = 65 Btu - 8 Btu = 57 Btu

Calculate the Change in Internal Energy (ΔU)

Now that we have the net heat added (Q_net) and the work done by the vapor (W), we can calculate the change in internal energy (ΔU) using the first law of thermodynamics: ΔU = Q_net - W ΔU = 57 Btu - 5 Btu = 52 Btu

State the Final Answer

The change in energy of the water for this process is 52 Btu.