Thermodynamics I 1

Chapter 4

Energy Analysis of Closed Systems

Homework #4 Due: TBA

2

Problems: 4.5E 4.8 4.24 4.25 4.34 4.42 4.46

4.55 4.59E 4.70E 4.74 4.81 4.89

3

Objectives• 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.

• Relate the specific heats to the calculation of the changes in internal energy and enthalpy of ideal gases.

• Describe incompressible substances and determine the changes in their internal energy and enthalpy.

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

4

MOVING BOUNDARY WORK

Moving boundary work (P dV work): The expansion and compression work in a piston-cylinder device.

The work associated with a moving boundary is called

boundary work.

A gas does a differential amount of work Wb as it forces the piston to move by a differential amount ds.

Wb is positive for expansionWb is negative for compression

For each process we need to determine:

P f V ( )

5

The area under the process curve on a P-V diagram represents the boundary work.

The boundary work done during a process depends on the path followed as well as the end states.

The net work done during a cycle is the difference between the work done by the system and the work done on the system.

6

Constant pressure process

Constant volume process

If the volume is held constant, dV = 0, and the boundary work equation becomes:

P-V diagram for V = constant

P 1

2

V

P

V

2 1

P-V diagram for P = constant

Example- Isothermal Process of an Ideal Gas

7

Discuss Example 4-3 in class:

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

PmRT

V

𝑃 1𝑉 1=𝑃 2𝑉 2=𝑚𝑅𝑇

8

Polytropic process

C, and n are constants.

n is called polytropic exponent.

Polytropic process of an ideal gas:

When n = 1 :

Schematic and P-V diagram for a polytropic process.

Example

9

Discuss Example 4-4 in class:

10

ENERGY BALANCE FOR ALL SYSTEMS

Energy balance for any system undergoing any process

Energy balance in the rate form

For constant rates, the total quantities are related to the quantities per unit time as follows:

Energy balance per unit mass basis

Energy balance in differential form

Δ 𝐸=Δ𝑈+Δ𝐾𝐸+Δ𝑃𝐸

11

Energy balance when sign convention is used (i.e., heat input and work output are positive; heat output and work input are negative).

Various forms of the first-law relation for closed systems when sign convention is used.

The first law cannot be proven mathematically, but no process in nature is known to have violated the first law, and this should be taken as sufficient proof.

ENERGY BALANCE FOR CLOSED SYSTEMS

A closed system does not involve any mass flow across its boundaries, the energy balance for the closed system can be expressed in terms of heat and work interactions as:

12

For a cycle E = 0, thus Q = W.

ENERGY BALANCE FOR CLOSED SYSTEMS IN A CYCLE

13

Energy balance for a constant-pressure expansion or compression process (Example 4-5)

HWU b

For a constant-pressure expansion or compression process:

An example of constant-pressure process (example 4-5)

General analysis for a closed system undergoing a quasi-equilibrium constant-pressure process. Q is to the system and W is from the system.

Example

14

Discuss Example 4-6 in class: