Understanding Refrigeration Plant Calculations

This problem involves calculating the mass flow rate of a refrigerant in a system operating on an ideal vapor-compression refrigeration cycle. We are given the total refrigeration capacity and the refrigeration effect per unit mass of the refrigerant.

Key Information Provided:

• Refrigeration Capacity: 10 TR (Tons of Refrigeration)
• Refrigeration Effect (per kg): 100 kJ/kg
• Conversion Factor: 1 TR = 3.5 kW
• Refrigerant: R-12
• Cycle Type: Ideal Vapor-Compression

Converting Refrigeration Capacity to kW

First, we need to convert the refrigeration capacity from Tons of Refrigeration (TR) to kilowatts (kW) using the given conversion factor.

Total Refrigeration Capacity ($Q_{dot}$) = Refrigeration Capacity in TR $\times$ Conversion Factor

$$Q_{dot} = 10 \text{ TR} \times 3.5 \text{ kW/TR}$$

$$Q_{dot} = 35 \text{ kW}$$

Since 1 kW is equal to 1 kJ/s, the total refrigeration capacity is 35 kJ/s.

Calculating Mass Flow Rate

The total refrigeration capacity ($Q_{dot}$) is the product of the mass flow rate of the refrigerant ($\dot{m}$) and the refrigeration effect produced per unit mass ($q_{effect}$).

The formula is:

$$Q_{dot} = \dot{m} \times q_{effect}$$

We need to find the mass flow rate ($\dot{m}$). Rearranging the formula, we get:

$$\dot{m} = \frac{Q_{dot}}{q_{effect}}$$

Step-by-Step Calculation:

1. Substitute the known values into the formula:

   $$Q_{dot} = 35 \text{ kJ/s}$$

   $$q_{effect} = 100 \text{ kJ/kg}$$

2. Calculate the mass flow rate:

   $$\dot{m} = \frac{35 \text{ kJ/s}}{100 \text{ kJ/kg}}$$

   $$\dot{m} = 0.35 \text{ kg/s}$$

Conclusion

The calculated mass flow rate of the refrigerant required to achieve a 10 TR capacity with a refrigeration effect of 100 kJ/kg is 0.35 kg/s. This matches one of the provided options.