Question

Refrigerant-134a at \(1.4 \mathrm{MPa}\) and \(90^{\circ} \mathrm{C}\) is throttled to a pressure of 0.6 MPa. The temperature of the refrigerant after throttling is \((a) 22^{\circ} \mathrm{C}\) \((b) 56^{\circ} \mathrm{C}\) \((c) 82^{\circ} \mathrm{C}\) \((d) 80^{\circ} \mathrm{C}\) \((e) 90^{\circ} \mathrm{C}\)

Short answer

a) 42°C b) 53°C c) 68°C d) 85°C e) 94°C

Step-by-step solution

Understand the throttling process

Throttling is an isenthalpic process, meaning that there is no change in enthalpy (h) during the process. The significance of this is that we can use the initial state (pressure and temperature) to find the initial enthalpy, and then use that constant enthalpy value to determine the final temperature at the given final pressure.

Determine initial enthalpy

First, we need to find the initial enthalpy of the refrigerant at the given conditions, which are 1.4 MPa and 90°C. Use the property tables (or appropriate software/tool) for Refrigerant-134a to find the initial enthalpy, \(h_1\).

Apply the constant enthalpy condition

Since the throttling process is isenthalpic, the enthalpy will not change throughout the process. Therefore, the final enthalpy \(h_2\) will be the same as the initial enthalpy, \(h_1\). So, we have: $$h_2 = h_1$$

Determine the final temperature

Now that we have the final enthalpy \(h_2\), we can use the property tables (or appropriate software/tool) for Refrigerant-134a again to find the temperature of the refrigerant at the final given pressure of 0.6 MPa and the final enthalpy \(h_2\). This will give us the final temperature, \(T_2\): $$T_2 = f(0.6 \text{ MPa}, \ h_2)$$

Compare the final temperature with the given options

Once we have determined the final temperature, we can compare it to the given options (a) through (e) to select the correct answer.

Key concepts

Isenthalpic Process

In thermodynamics, an isenthalpic process is a process in which the enthalpy of the system remains constant; there is no change in heat content. This is a typical characteristic of a throttling process like the expansion of refrigerant through an expansion valve or a capillary tube in refrigeration cycles.

During the throttling process, even though there might be significant changes in pressure and temperature, the enthalpy before and after the expansion stays the same. This is because the process is adiabatic (no heat transfer with the surroundings) and no work is done on or by the system. For example, in the exercise, Refrigerant-134a passes through a throttling device, changing pressure without altering its enthalpy.

Enthalpy

Enthalpy, often denoted as H or simply as h, is a measure of the total heat content in a thermodynamic system. It is the sum of the internal energy of the system plus the product of pressure and volume. The formula for enthalpy can be expressed as:
\[ H = U + PV \]
where U represents the internal energy, P is the pressure, and V is the volume. In a throttling process, since enthalpy is conserved, the exercise involves using enthalpy values to determine the temperature after the process by referencing the initial conditions provided.

Refrigerants

Refrigerants are fluids used in the refrigeration cycle to absorb and release heat, thereby enabling the cooling effect. Common refrigerants include Chlorofluorocarbons (CFCs), Hydrochlorofluorocarbons (HCFCs), and more environmentally friendly alternatives such as Refrigerant-134a. Refrigerants have unique thermodynamic properties, which are considered when designing refrigeration systems.

The choice of a refrigerant is critical, as it affects the efficiency, operating pressures, and environmental impact of a refrigeration system. In our exercise, the refrigerant used is Refrigerant-134a, which is known for its relatively low global warming potential and is commonly used as a replacement for the more ozone-depleting refrigerants.

Pressure-Enthalpy Diagram

A pressure-enthalpy diagram is a graphical representation of a refrigerant's thermodynamic properties. This tool is incredibly useful for engineers and technicians when analyzing refrigeration cycles. It plots the enthalpy of a refrigerant against the pressure level.

The diagram provides key information such as saturation temperatures, boiling and condensation points, and isentropic lines (lines of constant entropy). The diagram becomes especially valuable in visualizing what occurs during a throttling process, where a horizontal line is drawn at a constant enthalpy level to depict the isenthalpic process. For instance, in the given exercise, this diagram could assist in predicting the temperature after the Refrigerant-134a is throttled to a lower pressure.