A rigid container with a volume of 2 m3 contains twenty kilograms of refrigerant 134aat an initial pressure of 240 kPa. The container is cooled until the pressure of therefrigerant is 100 kPa. Determine:a) The initial temperature of the refrigerant; (5 marks)b) The final state (i.e., compressed liquid, saturated liquid, saturated mixtureetc.) of the refrigerant, giving your reasoning; and (3 marks)c) The heat transfer associated with the process. (14 marks)d) Sketch the process on a P-v diagram. (3 marks)
Question
A rigid container with a volume of 2 m3 contains twenty kilograms of refrigerant 134aat an initial pressure of 240 kPa. The container is cooled until the pressure of therefrigerant is 100 kPa. Determine:a) The initial temperature of the refrigerant; (5 marks)b) The final state (i.e., compressed liquid, saturated liquid, saturated mixtureetc.) of the refrigerant, giving your reasoning; and (3 marks)c) The heat transfer associated with the process. (14 marks)d) Sketch the process on a P-v diagram. (3 marks)
Solution
Sure, let's solve this step by step:
a) To find the initial temperature of the refrigerant, we need to use the ideal gas law equation, which is PV = mRT, where P is the pressure, V is the volume, m is the mass, R is the specific gas constant, and T is the temperature. The specific gas constant for refrigerant 134a is 0.0815 kJ/kg.K.
So, rearranging the equation to solve for T, we get T = PV / mR. Substituting the given values, we get T = (240 kPa * 2 m^3) / (20 kg * 0.0815 kJ/kg.K) = 294.5 K.
b) The final state of the refrigerant can be determined by looking at the pressure-temperature (P-T) diagram for the refrigerant. At 100 kPa, the refrigerant is in the saturated liquid-vapor mixture region.
c) To find the heat transfer associated with the process, we need to know the specific heat capacities of the refrigerant at the initial and final states. However, this information is not provided in the question.
d) On a P-v diagram, the process would be represented as a horizontal line from the initial state to the final state, as the volume is constant (rigid container) and the pressure decreases. The initial state is at a higher pressure and the final state is at a lower pressure.
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