Question

Consider a sealed can that is filled with refrigerant134a. The contents of the can are at the room temperature of \(25^{\circ} \mathrm{C} .\) Now a leak develops, and the pressure in the can drops to the local atmospheric pressure of \(90 \mathrm{kPa}\). The temperature of the refrigerant in the can is expected to drop to (rounded to the nearest integer \((a) 0^{\circ} \mathrm{C}\) (b) \(-29^{\circ} \mathrm{C}\) \((c)-16^{\circ} \mathrm{C}\) \((d) 5^{\circ} \mathrm{C}\) \((e) 25^{\circ} \mathrm{C}\)

Short answer

Answer: \(-29^{\circ} \mathrm{C}\)

Step-by-step solution

The initial temperature of R-134a in the can is \(25^\circ C\), and the initial pressure is not required, as it does not affect the outcome of the problem. #Step 2: Determine the final pressure of the refrigerant#

The local atmospheric pressure is \(90 \mathrm{kPa}\), to which the pressure in the can will drop as a leak develops. #Step 3: Find the saturation temperature corresponding to the final pressure#

We need to refer to a saturation table for R-134a to find the saturation temperature corresponding to the final pressure. Using the saturation table, we find that at a pressure of \(90 \mathrm{kPa}\), the saturation temperature, Tsat, is approximately \(-29.4^\circ C\). #Step 4: Determine the final temperature of the refrigerant in the can#

Given this information, it is clear that the refrigerant in the can will reach its saturation temperature. Therefore, the final temperature of the refrigerant in the can is approximately \(-29.4^\circ C\), which when rounded to the nearest integer is \(-29^\circ C\). The correct answer is (b) \(-29^{\circ} \mathrm{C}\).

Key concepts

Saturation Temperature

Understanding saturation temperature is essential in the study of thermodynamics, especially when dealing with refrigeration and air conditioning systems. Saturation temperature is the temperature at which a substance changes phase at a given pressure. For instance, at normal atmospheric pressure, water boils at 100°C, which is its saturation temperature.

In the case of refrigerants like R-134a, the saturation temperature is important because it tells us the temperature at which the refrigerant will start boiling or condensing at a particular pressure. For a sealed system like a refrigerant can, once a leak causes the pressure to drop to the local atmospheric pressure, the refrigerant changes phase to maintain its saturation temperature for that specific reduced pressure.

Local Atmospheric Pressure

Local atmospheric pressure can have a significant impact on phase changes for substances like refrigerants. The Earth's atmosphere exerts pressure on everything at surface level, which we refer to as atmospheric pressure. This pressure can vary depending on altitude, weather conditions, and temperature. Standard atmospheric pressure at sea level is about 101.3 kPa.

When the pressure in a system like a refrigerant can drops to match the local atmospheric pressure, the conditions for the refrigerant inside change drastically. If this pressure is below the initial pressure of the refrigerant, the refrigerant may start boiling off until its pressure decreases enough for the boiling to cease, reaching a new equilibrium at a lower saturation temperature.

R-134a Refrigerant Properties

Refrigerant R-134a, or 1,1,1,2-Tetrafluoroethane, is a common refrigerant used in various cooling applications due to its convenient thermodynamic properties and its relatively low impact on the environment compared to older refrigerants like R-12.

R-134a operates efficiently over a wide range of temperatures and pressures, making it suitable for use in domestic and automotive refrigeration systems. It has a relatively low boiling point, which allows it to absorb heat from the environment at lower temperatures. Consequently, when analyzing problems involving R-134a, one must take into account these properties, particularly the refrigerant's saturation temperature at various pressures, as demonstrated in our exercise. Moreover, R-134a's properties are well-documented in saturation tables, which engineers and technicians use to determine its behavior under different temperature and pressure conditions.