Question

A large refrigeration plant is to be maintained at \(-15^{\circ} \mathrm{C},\) and it requires refrigeration at a rate of \(100 \mathrm{kW}\) The condenser of the plant is to be cooled by liquid water, which experiences a temperature rise of \(8^{\circ} \mathrm{C}\) as it flows over the coils of the condenser. Assuming the plant operates on the ideal vapor-compression cycle using refrigerant-134a between the pressure limits of 120 and \(700 \mathrm{kPa}\), determine \((a)\) the mass flow rate of the refrigerant, \((b)\) the power input to the compressor, and (c) the mass flow rate of the cooling water.

Short answer

The analysis exercise involves calculating several key features of a refrigeration plant running on an ideal vapor-compression cycle that uses refrigerant-134a. Utilizing the given data along with properties of refrigerant-134a and the energy balance equations, results were determined for the mass flow rate of the refrigerant (8.33 kg/s), the power input to the compressor (161.27 kW), and the mass flow rate of the cooling water (2,990 kg/h).

Step-by-step solution

1. Calculate the enthalpies of states

To begin with, we should find the enthalpies of states. We know the pressure limits are 120 kPa (state 1) and 700 kPa (state 2), as given. We also know that the refrigeration plant is to be maintained at -15°C. Using the refrigerant-134a property table, locate the enthalpies at states 1 and 2: h1 = h(120 kPa, -15°C) = 234.26 kJ/kg h2 = h(700 kPa, -15°C) = 253.61 kJ/kg

2. Determine the mass flow rate of the refrigerant

We can determine the mass flow rate of the refrigerant by applying the energy balance equation: m_refrigerant = Q_refrigeration / (h1 - h2) where Q_refrigeration is the heat transfer rate (100 kW given in the problem), h1 is the enthalpy at state 1, and h2 is the enthalpy at state 2. Plug in the values: m_refrigerant = -100 / (234.26 - 253.61) = 8.33 kg/s The mass flow rate of the refrigerant is 8.33 kg/s.

3. Find the power input to the compressor

To find the power input to the compressor, we can use the following equation: W_compressor = m_refrigerant * (h2 - h1) Plug in the values: W_compressor = 8.33 * (253.61 - 234.26) = 161.27 kW The power input to the compressor is 161.27 kW.

4. Calculate the mass flow rate of the cooling water

To determine the mass flow rate of the cooling water, we can apply the energy balance equation: Q_out = m_water * C_water * ΔT_water where Q_out is the heat transfer rate from the refrigeration plant to the cooling water, m_water is the mass flow rate of the cooling water, C_water is the specific heat of water (4.184 kJ/kg°C), and ΔT_water is the temperature rise of the cooling water (8°C given in the problem). We know that the heat transfer rate is equal to the refrigeration rate, Q_refrigeration, so we can rearrange the equation for m_water: m_water = Q_refrigeration / (C_water * ΔT_water) Plug in the values: m_water = 100,000 W / (4.184 kJ/kg°C * 8°C) = 2,990 kg/h The mass flow rate of the cooling water is 2,990 kg/h.