Question

Refrigerant 134 a enters an insulated diffuser as a saturated vapor at 7 bars with a velocity of \(370 \mathrm{~m} / \mathrm{s}\). At the exit, the pressure is 16 bars and the velocity is negligible. The diffuser operates at steady state and potential energy effects can be neglected. Determine the exit temperature, in \({ }^{\circ} \mathrm{C}\).

Short answer

The exit temperature can be found by applying the steady-state energy equation, obtaining specific enthalpy values from the tables, and solving for the final temperature using negligible velocities.

Step-by-step solution

Understand the Problem

Identify the given information and what needs to be found. Refrigerant 134a enters as a saturated vapor at 7 bars with a velocity of 370 m/s, exits at 16 bars with negligible velocity, and the process is steady-state with negligible potential energy effects. We need to determine the exit temperature.

Apply the Steady-State Energy Equation

Use the steady-state energy equation for a control volume neglecting potential energy effects:

Determine Specific Enthalpies

Use the refrigerant R-134a tables to find the specific enthalpy at the inlet (7 bars as a saturated vapor) and the exit (16 bars).

Find Work and Heat Transfer

Recognize that the diffuser is insulated, so there is no heat transfer (Q = 0), and no work (W = 0) is done: Simplify the steady state energy Determine the exit temperature using the relationship between specific enthalpies and velocities.

Final Calculation

Using the simplified energy equation, solve for the exit temperature by substituting known values about enthalpies and velocities.

Key concepts

Refrigerant R-134a

Refrigerant R-134a is a commonly used refrigerant in air conditioning and refrigeration systems. It belongs to the hydrofluorocarbon (HFC) group and is known for its low ozone depletion potential. In this exercise, we focused on its behavior in a diffuser. As it enters the diffuser at 7 bars, it is in a state known as a 'saturated vapor'. This means it is at its boiling point and any additional energy will start to convert it into a liquid.

Understanding this behavior of refrigerant R-134a is crucial because its properties, such as pressure, temperature, and specific enthalpy, change significantly during the process. At the end of the diffuser, the pressure has increased to 16 bars, and we need to focus on how these properties help us determine the temperature at the exit.

Specific Enthalpy

Specific enthalpy is a measure of the total energy of a mass unit within the system. In simpler terms, it is the sum of the internal energy and the product of pressure and volume per unit mass. Specific enthalpy is standardly denoted by 'h' and its unit is typically kilojoules per kilogram (kJ/kg).

When working with refrigerants like R-134a, we often use property tables to find specific enthalpy values at different states. In this problem, we use the R-134a tables to find the specific enthalpy at the inlet (7 bars as a saturated vapor) and the outlet (16 bars). By doing so, we can apply the energy equation assuming no heat transfer or work is done in the diffuser. Simplifying this equation helps us use the change in specific enthalpy and velocities to determine the exit temperature.

Saturated Vapor

A saturated vapor refers to a state where a substance is at its boiling point at a given pressure and temperature. In this condition, the substance is a vapor that is ready to condense into a liquid with the slightest addition of heat or pressure. For R-134a at 7 bars, the refrigerant is in a saturated vapor condition, meaning it is entirely in the vapor phase at its boiling temperature.

The process of entering and exiting the diffuser involves significant changes in pressure and velocity. Initially, as a saturated vapor at 7 bars and high velocity, the refrigerant's specific enthalpy is found using the R-134a tables. As it exits at 16 bars and negligible velocity, we can assume the kinetic energy decreases and the potential energy remains negligible. These conditions allow us to focus on the enthalpy changes to determine the final temperature of the refrigerant.

Understanding saturated vapor states is essential for accurately predicting thermal behaviors in various engineering applications.