Question

A refrigerator is running with tetrafluoroethane (R1-34a) as the fluid and working based on the following cycle.

Saturated vapor at -12^oC is entering the compressor and leaving it at 40^oC. The superheated vapor after the compressor then condensed at constant pressure to saturated liquid, which ethers the “Joule-Thompson” throttling valve and back to the initial pressure. Assume your system is operating ideally, with a cooling load of 0.2 kW (200 J/s).

(a) Draw the cycle on the P-H diagram and showing each of the steps.

(b) Develop the energy balance for each step, and calculate heat and mechanical power per kg of fluid for each step.

(c)What is the flow rate of cooling fluid needed?

(d) What is the coefficient of performance (COP) of the refrigerator?

Answer 1

(a)

(b) The energy balance equation for condensation is given as,

Neglecting the Kinetic energy change and potential energy change the equation becomes,

Now the heat load is given as,

-ve sign indicates the heat is transferred from system to surrounding,

The energy balance equation for expansion valve is given as,

The energy balance equation for evaporator is given as,

The energy balance equation for compressor is given as,

Neglecting the Kinetic energy change and potential energy change the equation becomes,

(c) Understanding that fact during condensation and evaporation the temperature remains constant, and also Joule thomson expansion happen at constant enthalpy,

So we can write,

and The enthalpy of saturated vapour is found from the table as,

And the pressure of the vapour is

Since the compression is adiabatic

The heat capacity ratio needed for our temperature range is found out from the table as,

We can write,

The temperature at the outlet of the compressor is,

At temperature and Pressure the enthalpy is taken from table as,

Now this is the same pressure at which condensation is carried out, At this pressure the condensation temperature is found out as,

At this temperature the enthalpy of condensed saturated liquid is,

So the mass flow rate of cooling fluid is,

So the flow rate of cooling fluid needed is 3.141 kg/h

(d)

COP of the air refragation system is defined as,

is the heat absorbed in evaporator which can be found out as,

here (joule thomson expansion)

So,

The work done by the compressor can be calculated as,

So the COP of the system is 4.446