2b) Determine chemical formula of the following refrigerants

Here are the solutions to your problems:

2b) Determine chemical formula of the following refrigerants

• (i) R12: $\text{CCl}_2\text{F}_2$ (Dichlorodifluoromethane)
• (ii) R22: $\text{CHClF}_2$ (Chlorodifluoromethane)
• (iii) $\text{CO}_2$: $\text{CO}_2$ (Carbon dioxide)
• (iv) $\text{NH}_3$: $\text{NH}_3$ (Ammonia)
• (v) $\text{H}_2\text{O}$: $\text{H}_2\text{O}$ (Water)

3) A Freon 12 vapour compression system operating at a condenser temperature of $40^\circ\text{C}$ and evaporator temperature of $-5^\circ\text{C}$ develops 15 tons of refrigeration.

To solve this problem, a P-h diagram for Freon 12 (R12) is required to determine the specific enthalpy ($h$) and specific volume ($v$) values at different points in the cycle. Since the diagram is not provided, I will outline the steps and formulas.

Given Data:

• Refrigerant: Freon 12 (R12)
• Condenser temperature, $T_c = 40^\circ\text{C}$
• Evaporator temperature, $T_e = -5^\circ\text{C}$
• Refrigeration capacity, $Q_e = 15 \text{ tons of refrigeration (TR)}$

Conversion:
1 ton of refrigeration (TR) = 3.517 kW

$$Q_e = 15 \text{ TR} \times 3.517 \frac{\text{kW}}{\text{TR}} = 52.755 \text{ kW}$$

Cycle Points (from P-h diagram):

• State 1 (Evaporator outlet, compressor inlet): Saturated vapor at $T_e = -5^\circ\text{C}$.
  • Read $h_1$ (enthalpy), $v_1$ (specific volume), $s_1$ (entropy) from the diagram.
• State 2 (Compressor outlet, condenser inlet): Superheated vapor after isentropic compression from State 1 to the condenser pressure (corresponding to $T_c = 40^\circ\text{C}$).
  • Follow an isentropic line ($s_2 = s_1$) from State 1 to the condenser pressure. Read $h_2$.
• State 3 (Condenser outlet, expansion valve inlet): Saturated liquid at $T_c = 40^\circ\text{C}$.
  • Read $h_3$ from the diagram.
• State 4 (Expansion valve outlet, evaporator inlet): Liquid-vapor mixture after isenthalpic expansion from State 3.
  • $h_4 = h_3$.

Calculations:

• i) Mass flow rate of refrigerant circulated ($\dot{m}$): The refrigeration capacity is given by:

  $$Q_e = \dot{m}(h_1 - h_4)$$ $$\dot{m} = \frac{Q_e}{h_1 - h_4}$$

  Numerical value cannot be determined without $h_1$ and $h_4$ from the P-h diagram.

• ii) Theoretical piston displacement of the compressor ($\dot{V}$) and piston displacement per ton of refrigeration: The theoretical piston displacement is:

  $$\dot{V} = \dot{m} \cdot v_1$$

  Piston displacement per ton of refrigeration:

  $$\frac{\dot{V}}{\text{TR}} = \frac{\dot{m} \cdot v_1}{Q_e/\text{TR}}$$

  Numerical values cannot be determined without $\dot{m}$ and $v_1$ from the P-h diagram.

• iii) Theoretical horse power of the compressor ($W_c$) and horse power per ton of refrigeration: The theoretical compressor work is:

  $$W_c = \dot{m}(h_2 - h_1)$$

  To convert to horsepower (HP), use $1 \text{ HP} = 0.7457 \text{ kW}$:

  $$W_c (\text{HP}) = \frac{\dot{m}(h_2 - h_1)}{0.7457}$$

  Horse power per ton of refrigeration:

  $$\frac{W_c (\text{HP})}{\text{TR}} = \frac{W_c (\text{HP})}{Q_e/\text{TR}}$$

  Numerical values cannot be determined without $\dot{m}$, $h_1$, and $h_2$ from the P-h diagram.

• iv) Heat rejected in the condenser ($Q_c$): The heat rejected in the condenser is:

  $$Q_c = \dot{m}(h_2 - h_3)$$

  Numerical value cannot be determined without $\dot{m}$, $h_2$, and $h_3$ from the P-h diagram.

• v) Carnot COP and actual COP of the cycle:

  • Carnot COP ($\text{COP}_{\text{Carnot}}$): Convert temperatures to Kelvin: $T_e = -5^\circ\text{C} + 273.15 = 268.15 \text{ K}$ $T_c = 40^\circ\text{C} + 273.15 = 313.15 \text{ K}$

    $$\text{COP}_{\text{Carnot}} = \frac{T_e}{T_c - T_e} = \frac{268.15 \text{ K}}{313.15 \text{ K} - 268.15 \text{ K}} = \frac{268.15}{45} \approx \boxed{\text{5.959}}$$

  • Actual COP ($\text{COP}_{\text{actual}}$):

    $$\text{COP}_{\text{actual}} = \frac{Q_e}{W_c} = \frac{\dot{m}(h_1 - h_4)}{\dot{m}(h_2 - h_1)} = \frac{h_1 - h_4}{h_2 - h_1}$$

    Numerical value cannot be determined without $h_1$, $h_2$, and $h_4$ from the P-h diagram.