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Chapter 4: Problem 90

Propane vapor enters a valve at \(1.0 \mathrm{MPa}, 60^{\circ} \mathrm{C}\), and leaves at \(0.3 \mathrm{MPa}\). If the propane undergoes a throttling process, what is the temperature of the propane leaving the valve, in \({ }^{\circ} \mathrm{C}\) ?

Short Answer

Expert verified
The temperature of propane leaving the valve is the temperature corresponding to the enthalpy at 60掳C and 1 MPa, evaluated at 0.3 MPa.

Step by step solution

01

- Understand Throttling Process

In a throttling process, there is no work done, no heat transfer, and the enthalpy remains constant. Thus, the enthalpy before and after the valve is the same: \( h_1 = h_2 \).
02

- Identify Initial State Properties

From given data, the initial conditions of propane are: Pressure, \( P_1 = 1.0 \, \text{MPa} \), Temperature, \( T_1 = 60^{\circ} \, \text{C} \).
03

- Use Propane Property Tables or Software

Using propane property tables or appropriate software, find the specific enthalpy \( h_1 \) that corresponds to \( P_1 = 1.0 \, \text{MPa} \) and \( T_1 = 60^{\circ} \, \text{C} \).
04

- Apply Constant Enthalpy Condition

Since enthalpy remains constant through the throttling process, set the enthalpy at the exit state equal to the initial enthalpy: \( h_2 = h_1 \).
05

- Determine Exit State Properties

With the final pressure given as \( P_2 = 0.3 \, \text{MPa} \), use property tables or software to find the temperature \( T_2 \) corresponding to \( P_2 \) at the same enthalpy \( h_2 \).
06

- Conclude the Temperature

The temperature leaving the valve, \( T_2 \), can now be read from the property table or software result.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

enthalpy
Enthalpy is a key concept in thermodynamics, and it is especially important in processes like throttling. Enthalpy, represented by the symbol 'h', refers to the total heat content of a system. In mathematical terms, it is the sum of the internal energy and the product of pressure and volume: \[ h = U + PV \]. During a throttling process, enthalpy remains constant. This means the enthalpy before the throttling process is equal to the enthalpy after the process. This is crucial for solving problems where no heat is exchanged with the environment and no work is done, such as when gas flows through a valve.
propane properties
Propane, a common hydrocarbon, is used in various industrial and heating applications. It exists in both liquid and vapor states and transitions between these states based on pressure and temperature conditions. Specific properties of propane, such as specific enthalpy, need to be known to solve thermodynamic problems. These properties are often found in thermodynamic property tables or software. For example, at an initial state of 1.0 MPa and 60掳C, the specific enthalpy 'h' can be determined from such resources, which is essential for applying the constant enthalpy condition in throttling processes.
pressure-temperature relationship
The pressure-temperature relationship of gases is pivotal in thermodynamics. This relationship describes how the pressure of a gas changes with temperature if other conditions, like volume, are held constant. In a throttling process, despite the drop in pressure, the temperature doesn't follow this simple relationship due to the constant enthalpy condition. Therefore, when propane exits a valve at a lower pressure, pressure alone isn't sufficient to determine the temperature. We must reference thermodynamic property tables or software with both pressure and enthalpy data to determine the exit temperature.
thermodynamic property tables
Thermodynamic property tables are essential tools for solving problems in thermodynamics. These tables provide data for properties like pressure, temperature, volume, specific enthalpy, and specific entropy for various substances, including propane. In our exercise, such a table helps find the specific enthalpy at an initial state of 1.0 MPa and 60掳C. After determining this value, we can use the table again at the exit pressure of 0.3 MPa to find the corresponding temperature, keeping the enthalpy constant. Therefore, mastering the use of these tables is critical for accurately solving thermodynamic problems.

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Most popular questions from this chapter

Liquid propane enters an initially empty cylindrical storage tank at a mass flow rate of \(10 \mathrm{~kg} / \mathrm{s}\). Flow continues until the tank is filled with propane at \(20^{\circ} \mathrm{C}, 9\) bar. The tank is \(25 \mathrm{~m}\) long and has a \(4-\mathrm{m}\) diameter. Determine the time, in minutes, to fill the tank.

A rigid copper tank, initially containing \(1 \mathrm{~m}^{3}\) of air at \(295 \mathrm{~K}, 5\) bar, is connected by a valve to a large supply line carrying air at \(295 \mathrm{~K}, 15\) bar. The valve is opened only as long as required to fill the tank with air to a pressure of 15 bar. Finally, the air in the tank is at \(310 \mathrm{~K}\). The copper tank, which has a mass of \(20 \mathrm{~kg}\), is at the same temperature as the air in the tank, initially and finally. The specific heat of the copper is \(c=0.385 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\). Assuming ideal gas behavior for the air, determine (a) the initial and final mass of air within the tank, each in \(\mathrm{kg}\), and (b) the heat transfer to the surroundings from the tank and its contents, in kJ, ignoring kinetic and potential energy effects.

Air modeled as an ideal gas enters a well-insulated diffuser operating at steady state at \(270 \mathrm{~K}\) with a velocity of \(180 \mathrm{~m} / \mathrm{s}\) and exits with a velocity of \(48.4 \mathrm{~m} / \mathrm{s}\). For negligible potential energy effects, determine the exit temperature, in \(\mathrm{K}\).

Refrigerant 134 a enters a compressor operating at steady state as saturated vapor at \(0.12 \mathrm{MPa}\) and exits at \(1.2 \mathrm{MPa}\) and \(70^{\circ} \mathrm{C}\) at a mass flow rate of \(0.108 \mathrm{~kg} / \mathrm{s}\). As the refrigerant passes through the compressor, heat transfer to the surroundings occurs at a rate of \(0.32 \mathrm{~kJ} / \mathrm{s}\). Determine at steady state the power input to the compressor, in \(\mathrm{kW}\).

If a kitchen-sink water tap leaks one drop per second, how many gallons of water are wasted annually? What is the mass of the wasted water, in lb? Assume that there are 46,000 drops per gallon and that the density of water is \(62.3 \mathrm{lb} / \mathrm{ft}^{3}\).
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