TRC2200: Thermo Fluids & Power Systems

LECTURE 16

Energy Analysis of Closed Systems

Lecturer: Alpha Agape Gopalai

• For any process, the first law of thermodynamics dictates

Recap: Energy Balance for a Closed System

• Examine the moving boundary work or P dV work commonly encountered in reciprocating devices such as automotive engines and compressors.

• Identify the first law of thermodynamics as simply a statement of the conservation of energy principle for closed (fixed mass) systems.

• Develop the general energy balance applied to closed systems.

• Define the specific heat at constant volume and the specific heat at constant pressure.

• Solve energy balance problems for closed (fixed mass) systems that involve heat and work interactions for general pure substances, ideal gases, and incompressible substances.

Overview

• Moving boundary work is one form of mechanical work associated with a moving boundary.

• Consider a gas undergoing a quasi-equilibrium expansion process in a piston cylinder device.

Moving Boundary Work

• Therefore, for process 1-2, total boundary work is

Moving Boundary Work

Note: We assume that the process is in quasi equilibrium

• Boundary work is dependent on path. Area under each process curve is different.

Moving Boundary Work• In a cycle, net work is equal to

the area enclosed.

• A rigid tank contains air at 500 kPa and 150 oC. As a result of heat transfer to the surroundings, the temperature and pressure inside the tank drop to 650C and 400 kPa, respectively. Determine the boundary work done during this process.

Time to Think

• A rigid tank contains air at 500 kPa and 150 oC. As a result of heat transfer to the surroundings, the temperature and pressure inside the tank drop to 650C and 400 kPa, respectively. Determine the boundary work done during this process.

Time to Think

Isomeric systemOR

Isochoric

• A frictionless piston-cylinder device contain 5 kg of steam at 400 kPaand 200oC. Heat is now transfer to the steam until the temperature reaches 250oC. If the piston is not attached to a shaft and its mass is constant, determine the work done of the steam during this process

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• A frictionless piston-cylinder device contain 5 kg of steam at 400 kPaand 200oC. Heat is now transfer to the steam until the temperature reaches 250oC. If the piston is not attached to a shaft and its mass is constant, determine the work done of the steam during this process

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Isobaric system

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• A piston cylinder device initially contains 0.4 m3 of air at 100 kPa and 80oC. The air is now compressed to 0.1 m3 in such way that the temperature inside the cylinder remains constant. Determine the work done during the process.

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• A piston cylinder device initially contains 0.4 m3 of air at 100 kPa and 80oC. The air is now compressed to 0.1 m3 in such way that the temperature inside the cylinder remains constant. Determine the work done during the process.

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• Positive work (sign) indicates that the work is done by the system

• Negative work (sign) indicates that the work is done on the system

• Actual expansion and compression processes of gases are often polytropic. i.e. PVn=constant• When n = 1, then PV = constant, which is an expression for the

isothermal process.

Moving Boundary Work

A piston cylinder device contains 25 g of saturated water vapor that is maintained at a constant pressure of 300 kPa. A resistance heater is turned on. Heat loss of 3.7 kJ occurs.

a) Show that boundary work and change of internal energy can be combined into change of enthalpy.

b) Find the final temperature

Time to Think..

What is our first course of action?

Step 1: Problem statement. Open vs closed system?Step 2: Schematics. System, Boundary and Surrounding Interactions.

A piston cylinder device contains 25 g of saturated water vapor that is maintained at a constant pressure of 300 kPa. A resistance heater is turned on. Heat loss of 3.7 kJ occurs.

Time to Think..

This is a:

1. Isobaric System2. Closed System

Step 3: Assumptions & Approximations

We are not given any information about elevation or velocity. Therefore, we can assume the system to be a stationary system

A piston cylinder device contains 25 g of saturated water vapor that is maintained at a constant pressure of 300 kPa. A resistance heater is turned on. Heat loss of 3.7 kJ occurs.

Time to Think..

Step 4: Physical Laws

Isobaric System

A piston cylinder device contains 25 g of saturated water vapor that is maintained at a constant pressure of 300 kPa. A resistance heater is turned on. Heat loss of 3.7 kJ occurs.

Time to Think..

From Table A-4

Solving for h2

But how to use this information to solve for final temperature?

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A rigid tank is divided into two equal parts by a partition contains 5kg of water at 200 kPa and 25oC and the other side is evacuated. The partition is then removed, the water is allowed to exchange heat with its surroundings until the temperature in the tank returns to the initial value of 25oC. Determine (a) volume of water in the tank, (b) final pressure, (c) heat transfer from the process.

Time to Think..

What is our first course of action?

Step 1: Problem statement. Open vs closed system?Step 2: Schematics. System, Boundary and Surrounding Interactions.

A rigid tank is divided into two equal parts by a partition contains 5kg of water at 200 kPa and 25oC and the other side is evacuated. The partition is then removed, the water is allowed to exchange heat with its surroundings until the temperature in the tank returns to the initial value of 25oC. Determine (a) volume of water in the tank, (b) final pressure, (c) heat transfer from the process.

Time to Think..

This is a:

1. Isochoric or Isomeric System2. Closed System

Step 3: Assumptions & Approximations

We are not given any information about elevation or velocity. Therefore, we can assume the system to be a stationary system

Time to Think..

Step 4: Physical Laws

• An insulated rigid tank initially contains 0.7 kg of helium at 27oC and 350 kPa, A paddle wheel with a power rating of 0.015 kW is operated within the tank for 30 minutes. Determine (a) the final temperature, (b) the final pressure.

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• An insulated rigid tank initially contains 0.7 kg of helium at 27oC and 350 kPa, A paddle wheel with a power rating of 0.015 kW is operated within the tank for 30 minutes. Determine (a) the final temperature, (b) the final pressure.

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Assumptions:• Helium is an ideal gas• Stationary System, delta KE = delta PE = 0• Volume is constant, no boundary work• Insulated tanks, adiabatic system• Specific heat at constant volume – Table A2.

Final Temperature Final Pressure

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• a

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• a

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• Final Temperature, T3

• Total work done, W13

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• Heat Transfer, Q13

OR

• Using Table A-21 to find u Using Table A-2 to find Cv

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• Moving Boundary Work

• Energy Balance for Closed System

• Internal energy, enthalpy and specific heats of ideal gases

Lecture Summary

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