A single cylinder 12 ton vapour compression refrigeration system based on R-22 operates between the temperatures of -10°C and 40°C. Given values of enthalpy are 246.5, 294.5 and 97... A single cylinder 12 ton vapour compression refrigeration system based on R-22 operates between the temperatures of -10°C and 40°C. Given values of enthalpy are 246.5, 294.5 and 97.65 kJ per kg for the evaporator process, compressor process, and expansion process respectively. Draw the p-h diagram for the same and calculate CoP, mass flow rate and power required of the system. Read more

Steps to Solve

1. Determine the Cooling Capacity The cooling capacity (Q) is given as 12 tons. Convert tons to kW using the conversion factor: $$ 1 \text{ ton} = 3.517 \text{ kW} $$ Thus, $$ Q = 12 \text{ tons} \times 3.517 \text{ kW/ton} = 42.204 \text{ kW} $$

2. Calculate the Coefficient of Performance (CoP) The Coefficient of Performance (CoP) is calculated using the formula: $$ \text{CoP} = \frac{Q}{W} $$ Where ( W ) is the work done by the compressor.

To find ( W ): $$ W = H_{compressor} - H_{evaporator} = 294.5 \text{ kJ/kg} - 246.5 \text{ kJ/kg} = 48.0 \text{ kJ/kg} $$

Thus we can calculate CoP: $$ \text{CoP} = \frac{42.204 \text{ kW}}{W} $$

3. Calculate the Mass Flow Rate (MFR) Mass flow rate can be determined using the equation: $$ \dot{m} = \frac{Q}{h_{evaporator}} $$ Substituting values: $$ \dot{m} = \frac{42.204 \text{ kW}}{246.5 \text{ kJ/kg}} = \frac{42.204 \text{ kW}}{0.2465 \text{ kW/kg}} \approx 171.99 \text{ kg/h} $$

4. Calculate the Power Required (P) The power required for the compressor can be calculated as: $$ P = \dot{m} \times W $$ Substituting values: $$ P = 0.17199 \text{ kg/s} \times 48.0 \text{ kJ/kg} = 8.25 \text{ kW} $$