Question

Goal Solve for the performance coefficient of a refrigerator using a fivestep process the includes: 1. Making a state table. 2. Making a process table. 3. Calculating the totals for Work, Heat, and Internal-Energy-Change. 4. Identifying the heat input (cold reservoir) and output (hot reservoir). 5. Calculating the performance coefficient of the refrigerator. Problem Shown in the figure to the right is a cyclic process undergone by a refrigerator. Your refrigerator shall use 10.0 moles of helium gas (monatomic). During the process a−>b, the volume increases by a factor of 3.0. Solution (1) Fill in the State Table (all pressures in Pascals, all volumes in cubic meters, all temperatures in K ). (2) Fill in the Process Table (all entries in Joules). (3) Find the Totals:

Work =
Heat =
dU=
​

J
J
J
​
(4) Find the heat input (from "cold reservoir") and the heat output (to "hot reservoir"): (5) Find the performance coefficient of the refrigerator: Coefficient =

Answer 1

To calculate the performance coefficient of a refrigerator, you need to create a state table and a process table, calculate the total work, heat, and internal energy change, and then find the heat input and output. Finally, you can calculate the coefficient of performance using the equation: Coefficient = Heat Absorbed / Work Input.

Step-by-step explanation:

Calculation of the Performance Coefficient of a Refrigerator:

1. Make a state table to record the properties of each stage of the refrigerator cycle. In this case, the state table includes pressure, volume, and temperature values.
2. Create a process table to calculate work, heat, and internal energy change for each process in the cycle. In this case, the process table will include the initial and final states of each process.
3. Calculate the total work, heat, and internal energy change by summing the values from the process table.
4. Identify the heat input from the cold reservoir and the heat output to the hot reservoir.
5. Calculate the performance coefficient of the refrigerator using the equation: Coefficient = Heat Absorbed / Work Input.

Example Calculation:

Given that the refrigerator removes 500 J of heat from the cold reservoir and discharges 800 J to the hot reservoir, the coefficient of performance can be calculated by dividing the heat absorbed (500 J) by the work input (unknown in this case).

Therefore, the coefficient of performance = 500 J / Work Input.

Answer 2

The coefficient of performance of a refrigerator is calculated using the ratio of heat removed from the cold reservoir to the work performed by the refrigerator, applying the first law of thermodynamics and considering the refrigeration cycle as a cyclical process.

Step-by-step explanation:

The student's question is related to the coefficient of performance of a refrigerator, which requires an understanding of the principles of thermodynamics. To calculate the coefficient, one must apply the first law of thermodynamics and understand what constitutes a cyclical process. The coefficient of performance for a refrigerator is the ratio of heat transfer from the cold reservoir to the work supplied. To solve problems like this, one must often make calculations based on the amount of work done and heat transferred during a refrigeration cycle.

Examples and Explanation

For instance, when given that a refrigerator has a coefficient of performance of 3.0 and requires 200 J of work per cycle (example 29), you would use the formula:

COP = Qc / W

where COP is the coefficient of performance, Qc is the heat removed from the cold reservoir, and W is the work done by the refrigerator. With a COP of 3.0 and work of 200 J, rearranging the formula gives:

Qc = COP × W = 3.0 × 200 J = 600 J

This means the refrigerator removes 600 J of heat from the cold reservoir per cycle. Additionally, the total heat discharge to the hot reservoir (Qh) can be calculated using the first law of thermodynamics:

Qh = Qc + W, thus Qh = 600 J + 200 J = 800 J