Calculate the required mass flow rate of the refrigerant in kg/s.

Steps to Solve

1. Calculate Solar Energy Input

First, we need to determine the total solar energy input to the collector:

$$ \dot{Q}_{\text{solar}} = \text{Area} \times \text{Solar Power} $$

Given:

• Area ( = 1000 , \text{m}^2 )
• Solar Power ( = 0.3 , \text{kW/m}^2 )

Now substituting the values:

$$ \dot{Q}_{\text{solar}} = 1000 , \text{m}^2 \times 0.3 , \text{kW/m}^2 = 300 , \text{kW} $$

2. Calculate Energy Absorbed by the Refrigerant

Since 60% of the solar input is absorbed by the refrigerant:

$$ \dot{Q}{\text{absorbed}} = 0.6 \times \dot{Q}{\text{solar}} $$

Substituting the value:

$$ \dot{Q}_{\text{absorbed}} = 0.6 \times 300 , \text{kW} = 180 , \text{kW} $$

3. Use the Energy Equation for the Refrigerant

From the first and second laws of thermodynamics, we can express the energy balance for the refrigerant passing through the solar collector:

$$ \dot{Q}_{\text{absorbed}} = \dot{m} \cdot (h_2 - h_1) $$

Where:

• ( \dot{m} ) = mass flow rate (kg/s)
• ( h_2 ) = specific enthalpy at state 2
• ( h_1 ) = specific enthalpy at state 1

4. Retrieve Enthalpy Values

Using refrigerant property tables or software for R-134a, find ( h_1 ) and ( h_2 ) at the given pressures and qualities. Assuming:

• For state 1 (p1=18 bar, x1=1): ( h_1 ) is found from saturated liquid vapour table.
• For state 2 (p2=7 bar, x2=0.9952): use the same method.

Let's assume:

• ( h_1 = 450 , \text{kJ/kg} )
• ( h_2 = 283.21 , \text{kJ/kg} ) (the exact values need referencing from the R-134a tables)

5. Solve for Mass Flow Rate

Rearrange the energy equation to find ( \dot{m} ):

$$ \dot{m} = \frac{\dot{Q}_{\text{absorbed}}}{h_2 - h_1} $$

Substituting the values:

$$ \dot{m} = \frac{180 \times 10^3 , \text{W}}{283.21 , \text{kJ/kg} - 450 , \text{kJ/kg}} $$

Calculating:

$$ \dot{m} = \frac{180 \times 10^3}{(283.21 - 450) \times 10^3} = \frac{180000}{-166.79 \times 10^3} $$

Calculate ( \dot{m} ).