Question

Air enters an air-conditioning system that uses refrigerant-134a at 30°C and 70 percent relative humidity at a rate of 4 m3/min. The refrigerant enters the cooling section at 700 kPa with a quality of 20 percent and leaves as saturated vapor. The air is cooled to 20°C at a pressure of 90kPa .

Determine the rate of dehumidification m˙w=   kg/min (Round to five decimal places)

Determine the rate of heat transfer Q˙out= kJ/min (Round to two decimal places)

Determine the mass flow rate of the refrigerant m˙R= kg/min (Round to three decimal places)

Answer 1

Some important assumptions to make while solving this problem are as follows

• The heat exchanger (evaporator) is 100% efficient
• The refrigerant stays at a constant pressure of 0.7 MPa during the heat exchange process
• The air stays at a constant pressure of 90 kPa during the heat exchange process.
• It is assumed that the air at the outlet has 100% Relative humidity. A theory supporting this assumption is that assuming air to be an ideal gas for inlet (30 DBT and 70% RH) and outlet (20 DBT and 100% RH). This equation holds true for the values of the properties at the 2 points.

From the pH chart for R 134a and the psychrometric chart at 90 kPa (988.5 m altitude), we can get a lot of vital information required to solve this problem from the data provided in the question. Please note that due to copyright and legal issues I am not allowed to post such charts directly from the internet. However, you can easily cross-verify from any random chart available.

Chart used	Data used	Data obtained	Value
R 134a pH chart	Saturation pressure 0.7 MPa, 0.2 quality	Enthalpy at inlet refrigerant h(ri) kJ/kg	265
R 134a pH chart	Saturation pressure 0.7 MPa, saturated vapour	Enthalpy at outlet refrigerant h(ro) kJ/kg	410
psychrometric chart	30 DBT, 70% RH	Enthalpy of air inlet h(ai) kJ/kg	84.46
psychrometric chart	30 DBT, 70% RH	The specific volume of air inlet v m3/kg	1
psychrometric chart	30 DBT, 70% RH	The absolute humidity of air inlet w(1) kg/kg	0.02118
psychrometric chart	20 DBT, 100% RH	Enthalpy of air outlet h(ao) kJ/kg	62.19
psychrometric chart	20 DBT, 100% RH	The absolute humidity of air outlet w(2) kg/kg	0.01659

Given the volume flow rate of air is V = 4 m3/min

PART A

The rate of dehumidification is the change in absolute humidity for the total mass flow rate of air. Thus it is given by

PART B

The rate of heat transfer is the total heat rejected by the air. This is obtained by multiplying the mass flow rate of air with the change in enthalpy.

PART C

The mass flow rate of the refrigerant can new obtained by balancing the heat exchange between the air and refrigerant. Thus

ANSWERS

• The rate of dehumidification is 0.01836 kg/min
• The rate of heat transfer is 89.08 kJ/min
• The mass flow rate of the refrigerant is 0.614 kg/min

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