1

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

2

MOVING BOUNDARY WORK

Moving boundary work (P dV work):

The expansion and compression work

in a piston-cylinder device.

Quasi-equilibrium process:

A process during which the system

remains nearly in equilibrium at all

times.

Wb is positive for expansion

Wb is negative for compression

3

The boundary

work done

during a process

depends on the

path followed as

well as the end

states.

The area under the process curve on a P-V

diagram is equal, in magnitude, to the work

done during a quasi-equilibrium expansion or

compression process of a closed system.

4

5 kPa

400 kPa

v, m3/kg

P,

kPa

400

Boundary Work for a constant-pressure

Boundary Work for a constant-pressure

• Example 4-2

A frictionless piston-cylinder device contains 5 kg of steam at 400 kpa and 200oC. Heat is now transferred 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 by the steam during this process.

• Solution

steam in a piston cylinder device is heated and the temperature rises at constant pressure. The boundary work done is to be determined.

Analysis:

Assumption:

Even though it isn’t explicitly stated, the pressure of the steam within the cylinder remains constant during this process since both the atmospheric pressure and the weight of the piston remain constant. Therefore, this is a constant-pressure process and, from equation 4-2 (Refer to the book).

5

•

6

7

What is the boundary

work for a constant-

volume process?

Boundary Work for a constant-Volume

•

8

9

10

Boundary Work for an Isothermal Compression Process

• Example 4-3

• 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 a way that the temperature inside the cylinder remains constant. Determine the work done during this process.

• Solution

air in a piston-cylinder device is compressed isothermally. The boundary work done is to be determined.

Analysis a sketch of the system and the P-V diagram of the process shown in Fig 4-8.

Assumption: at specified conditions, air can be considered to be an ideal gas since it is a high temperature and low pressure relative to its critical-point values To,

11

Boundary Work for an Isothermal Compression Process

Apply the equation of boundary work related to isothermal compression of ideal gas

12

13

SPECIFIC HEATS Specific heat at constant volume, cv: The

energy required to raise the temperature of

the unit mass of a substance by one degree

as the volume is maintained constant.

Specific heat at constant pressure, cp: The

energy required to raise the temperature of

the unit mass of a substance by one degree

as the pressure is maintained constant.

Constant-

volume and

constant-

pressure specific

heats cv and cp

(values are for

helium gas).

14

• The equations are valid for any

substance undergoing any process.

• cv and cp are properties.

• cv is related to the changes in internal

energy and cp to the changes in

enthalpy.

• A common unit for specific heats is

kJ/kg·°C or kJ/kg·K. Are these units

identical?

True or False?

cp is always greater than cv

Formal definitions of cv and cp.

15

Summary

• Moving boundary work

Wb for an isothermal process

Wb for a constant-pressure process

Wb for a polytropic process

• Specific heats

Constant-pressure specific heat, cp

Constant-volume specific heat, cv