Question

5. Saturated liquid R-134a enters an expansion valve at 40 C. The refrigerant leaves the expansion valve at 6 C. What is the specific volume at the exit

Answer 1

The specific volume of R-134a at the exit of the expansion valve is 0.014655 cubic meters per kilogram.

Step-by-step explanation:

From Thermodynamics, we know that expansion valves are devices that work at steady state, in which heat and work interactions are usually non-existent and changes in gravitational potential and translational kinetic energy. From First Law of Thermodynamics and the Principle of Mass Conservation we get that expansion valve is represented by the following model:

`\dot H_(in)-\dot H_(out) = 0` (Eq. 1)

`\dot m_(in)-\dot m_(out) = 0` (Eq. 2)

Where:

`\dot H_(in)`,
`\dot H_(out)` - Rates of change of inlet and output enthalpies, measured in kilowatts.

`\dot m_(in)`,
`\dot m_(out)` - Mass flow rates at inlet and outlet, measured in kilograms per second.

From definition of enthalpy and (Eq. 2), we simplify (Eq. 1) as follows:

`u_(in) + P_(in)\cdot \\u_(in) = u_(out) + P_(out)\cdot \\u_(out)` (Eq. 3)

Where:

`u_(1)`,
`u_(2)` - Specific internal energies at inlet and outlet, measured in kilojoules per kilogram.

`P_(1)`,
`P_(2)` - Inlet and outlet pressures, measured in kilopascals.

`\\u_(1)`,
`\\u_(2)` - Inlet and outlet specific volumes, measured in cubic meters per kilogram.

Now we get the following information from property charts:

Inlet (Saturated Liquid)

`T = 40\,^(\circ)C`

`P = 1017.1\,kPa`

`\\u = 0.0008720\,(m^(3))/(kg)`

`u = 107.39\,(kJ)/(kg)`

`h = 108.28\,(kJ)/(kg)`

`x = 0`

Outlet (Liquid-Vapor Mix)

`T = 6\,^(\circ)C`

`P = 362.23\,kPa`

`\\u = 0.014655\,(m^(3))/(kg)`

`u = 102.968\,(kJ)/(kg)`

`h = 108.28\,(kJ)/(kg)`

The specific volume of R-134a at the exit of the expansion valve is 0.014655 cubic meters per kilogram.