Ch. 2: Energy & 1st Law of Thermo

Closed Systems

Ch. 2: Energy & 1st Law of Thermo

Esys

Closed Systems

I. E, Energy (a property)

Mechanical Energy:

Kinetic Energy, Translational

Potential Energy, Gravitational

I. E, Energy

Internal Energy, U:

sum of microscopic forms of energy:

Electron and nuclear forces (atomic level)

Bonds in molecules

Kinetic Energy of molecules

Translation, rotation, vibration

Molecule to molecule forces (eg. H2O)

A change in Temperature (or sometimes pressure) or phase causes a change in U

Sensible heat: change of temperature of substance

Latent heat: change of phase of substance

u, specific internal energy:

I. E, Energy (continued)

Total Energy E:

specific energy e:

Height change z must be relative to the direction of gravity

Scalar: no associated direction

relative to a reference point

A property !!

Energy conversion between KE ad PE (pendulum swings)

I. E, Energy (continued)

Change in Energy:

II. Energy Transfers:

Energy transfer = flow of energy across a boundary of a system during a process

Q, Heat:

W, Work:

II. Energy Transfers, continued

Q and W can flow in and/or out, at several places

Q and W are NOT properties

they are path dependent

Qin Win

Qout

II. Energy Transfer by HEAT: Q

Heat vs. Thermal Energy vs. Temperature

Units (kJ, Btu)

Sign convention

Heat added to the system is positive

Heat removed from the system is negative

Adiabatic process: no heat transfer

Types of heat transfer modes Conduction

Convection

Radiation

II. Energy Transfer by HEAT: Q

2

1

2

1

2 2

Q: amount of energy transfer by heat (J, BTU)

: rate of heat transfer (W=J/s, BTU/h)

: heat flux, heat transfer rate per unit area (W/m , BTU/h.ft )

t

t

t

t

Q

q

Q Qdt

Q qdA

II. Energy Transfer by HEAT: Q

Heat is not a property, it is path dependent

2

2 1

1

The amount of energy transfer by heat for a process

Heat is not a property

Q Q Q Q

II. Energy Transfer by WORK: W

Units (kJ, Btu, ft-lbf)

Work is not possessed by a system-only measured as it crosses the system boundary

Sign convention:

positive if done by a system,

negative if done on a system

Many types of Work Mechanical

Electrical

Expansion/compression

II. Energy Transfer by Work: W

2

1

2

1

Work is not a property

= . (J, BTU)

: power (W=J/s, BTU/h)

=

s

s

t

t

W F ds

W

W Wdt

II. Work is path dependent

Work is not a property

II. Work is path dependent

III. 1st Law of Thermodynamics

Closed System

(integrated over time):

Qin Wout E

Example 2.1:

A 1 kg metal weight that is initially 1 m above the ground is connected by a cable

through a frictionless pulley to a smaller

mass. The 1 kg mass is dropped from rest

and does 5 Joules of work as it lifts the

smaller weight.

Determine the speed at which the 1 kg mass hits the ground.

III. 1st Law of Thermodynamics, cont.

Closed System (Instantaneous):

Qin Wout E

IV. Cycles

Cycle: a series of

processes that begin and

end at the same state

IV. Cycles, cont.

1st Law Energy Balance

Equation for a cycle:

0 cycleE

cyclecycle WQ

or

Example 2.3:

A closed system (stationary) goes through a 3-process cycle beginning with U1 = 100 kJ.

1500 J of heat is added to the system during process 1-2 until

the internal energy increases to U2 = 200 kJ.

Process 2-3 is adiabatic as 10 kJ work is done on the system.

No work is done during process 3-1.

Find U, Q, and W for each process.

Process U Q W

1-2

2-3

3-1

II. Types of Work and Power

Mechanical Work:

Mechanical Power:

.mechW F ds

?dt

dsFWmech

FV

2

2

1VACF fddrag

WeightfFrolling *rollingdrag FFF where

II. Types of Work and Power

Rotational Mechanical Power (Shaft Power):

rotW

sec

min

rev

rad

min

rev

60

1

1

2 RPM

II. Types of Work and Power

Electrical Power:

E* i

elecW

dtWWt

AmpVoltWatt 1*11

II. Types of Work and Power

Fluid Power:

Recall: Relating Power and Work :

VpW fluid *

dtWWt

t

WWaverage

II. Types of Work and Power

Expansion/Compression Work:

II. Expansion / Compression Work:

- Common form of work for a

gas in a piston/cylinder device

V, p

y

cylinder

piston

gas

II. Expansion / Compression Work

To move the piston up (expand):

FdsW

?FwithF

II. Expansion / Compression Work

pAdsW

?AdsandF

pAF

II. Expansion / Compression Work

pdVW

dVAds

II. Expansion / Compression Work

W on p-V diagram

Work = ?

pdVWV

P

Work =

area under curve

V = constant

pV = constant

II. pdV Work: 4 cases

p = constant

pVn = constant (polytropic)

pVn = constant (polytropic)

II. calculating pdV work for 4 cases

V = constant

pV = constant

p = constant

Example 2.4:

0.41 lb of air in a piston/cylinder device goes through a constant pressure (p = 20

lbf/in2) heat addition process as the

volume changes from 5 ft3 to 6.52 ft

3.

Find the work during this process.

Example 2.5:

Nitrogen, which behaves as an ideal gas, is compressed in a piston cylinder device

as temperature is held constant at 27C.

The work required during compression is 7000 J.

The initial pressure and volume are 100 kPa and 0.1 m

3.

Find (a) the final volume and (b) the heat

during this process.

Example 2.6:

0.05 kg of air

expands in a piston cylinder device until

the final volume is 4 times the initial volume.

The initial pressure and volume are 400 kPa and 0.0144 m

3, and

the expansion is polytropic with n = 1.4. Find the work during this process.

IV. Cycles, cont.

Thermal Reservoir: A large mass that can accept or reject heat without

changing temperature

(also called thermal energy

SOURCE or SINK)

at TL

at TH

IV. Cycles, cont.

Thermal Reservoirs:

Thermal cycles operate

between two thermal

reservoirs

IV. Cycles, cont.

1. Power Cycle

Objective:

2a. Refrigeration Cycle

Objective:

2b. Heat Pump Cycle

Objective

IV. Thermal Cycles 3 types

IV. Cycles

1. Power

Cycle

1. Power Cycle

Objective: to produce work

(power), Wnet,out

By using heat added from a high-temperature reservoir

(QH from TH) QH is IN

And rejecting heat to a low-temperature reservoir

(QL to TL) QL is OUT

Power

Cycle

1. Power Cycle

- Power Cycle Energy Balance

Power

Cycle

- Power Cycle Performance

Refrigeration

Objective: to keep LOW

temperature reservoir

cool by removing QL

R

High temp Reservoir

Low temp Reservoir

Driven by Work (Power) put

into the cycle

(compressor)

Refrigeration

R

High temp Reservoir

Low temp Reservoir

- Refrigeration Cycle Performance

- Refrigeration Cycle Energy Balance

Heat Pump

Objective: to keep HIGH

temperature reservoir

warm by adding QH

High temp Reservoir

Low temp Reservoir

R or

HP

HP

Driven by Work (Power) put into

the cycle (compressor)

Heat Pump

High temp Reservoir

Low temp Reservoir

R or

HP

HP

- Heat Pump Cycle Energy Balance

- Heat Pump Cycle Performance

1. Power Cycle

2a. Refrigeration Cycle

2b. Heat Pump Cycle

Example 2.7:

A 600 MW steam power plant is cooled by water from a nearby river.

The thermal efficiency of the plant is 40%. Find the rate of heat rejection from the plant to

the river.

Example 2.8:

A household refrigerator has a coefficient of performance of 1.2.

Heat transfer to the refrigerated space through the insulation and due to opening of the

refrigerator doors is 60 kJ/min.

Find

the electric power consumed by the refrigerator and

the rate of heat transfer to the kitchen air from the refrigerator.

Example 2.9:

A heat pump is used to maintain the air in a home at 69F when

the outside temperature is just below freezing.

Heat loss from the home through doors, windows, the roof, and the walls is 36,000

Btu/hr.

What is the coefficient of performance of the heat

pump if it consumes electrical power at the rate of

1 kW.