Question

Shown in the figure below is the cycle undergone by a Refrigerator. Your refrigerator runs using 39.20 moles of diatomic Hydrogen gas. At point a in the figure, the temperature is Ta = 285 Kelvin and the pressure is Pa = 247000 Pascals. During the process a→b, the Pressure of the system Quadruples. Thermo-HeatFridge2 Determine all the following: CV = Joules/(mole · K); CP = Joules/(mole · K); = STATE P (Pa) V (m3) T (K) a b c PROCESS W (J) Q (J) ΔU (J) a→b b→c c→a Total Qhot = Joules Qcold = Joules Performance Coefficient =

Answer 1

Determine thermodynamic parameters, processes, and quantities for the given refrigerator cycle, including CV, CP, state points, work, heat, and the performance coefficient. Additional data may be required for a complete analysis.

To determine the thermodynamic parameters and quantities for the given refrigerator cycle, we need to follow the processes described in the figure and apply the appropriate formulas.

1. CV (Specific Heat at Constant Volume):

The specific heat at constant volume (CV) is calculated using the ideal gas law and the relationship
`\(C_v = (R)/(\gamma - 1)\)`, where (R) is the gas constant and
`\(\gamma\)` is the heat capacity ratio.

2. CP (Specific Heat at Constant Pressure):

For diatomic hydrogen,
`\(CP - CV = R\)`, and thus CP = CV + R. This relationship is derived from the first law of thermodynamics.

3. State Point P (a):

Given values are
`\(T_a = 285 \, \text{K}\)`,
`\(P_a = 247,000 \, \text{Pa}\)`, and
`\(n = 39.20 \, \text{moles}\)`. Use the ideal gas law PV = nRT to calculate the volume
`(\(V_a\))` at point a.

4. Process a→b:

During this process, the pressure quadruples
`(\(P_b = 4 * P_a\))`. Use the ideal gas law to find the new temperature
`(\(T_b\))`, and calculate the work
`(\(W_(ab)\))` and heat
`(\(Q_(ab)\))` using thermodynamic relations.

5. Process b→c:

The figure does not provide enough information for a direct calculation of
`\(T_c\)`. Additional data or assumptions are needed to proceed with the analysis.

6. Process c→a:

Similar to process b→c, additional information is required for a direct calculation of
`\(T_a\)`.

7. Total Heat Absorbed and Released (Qhot and Qcold):

Determine the total heat absorbed
`(\(Q_{\text{hot}}\))` and released
`(\(Q_{\text{cold}}\))` during the entire cycle.

8. Performance Coefficient:

Calculate the performance coefficient using the formula
`\(COP = \frac{Q_{\text{cold}}}{W_{\text{net}}}\)`.

Given the nature of the refrigerator cycle and the lack of complete information, assumptions or additional data might be necessary for a comprehensive analysis.