Exp. #1-7 : Measurement of the Characteristics of the Heat...

General Physics Laboratory – Experiment Report

1st Semester, Year 2018

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Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2018-05-08

Exp. #1-7 : Measurement of the Characteristics of the Heat Engine

by Using a Computer Interface

Student's

Mentioned

Items

Student ID Major Name Team No. Experiment Lecturer

Experiment Class Date Submission Time Submission PlaceIntroductory Physics Office

Report Box #

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Lecturer's

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Submission Time/Place Check Experiment Report Score Evaluation Completion Sign

50



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1. Objective

In this experiment, the characteristics of the heat engine operated by the reversible cycle consisting of isothermal and isobaric processes is measured and how

the 1st law of thermodynamics is applied to the heat engine is investigated.

2. Theory

(1) The 1st law of thermodynamics and the internal energy

If the heat is transferred to the ideal gas with the pressure , the gas does

work through the volume change and undergoes the internal energy

change int through the temperature change. In this situation, the following

relation can be made.

int int (Eq. 1)

This relation is referred to as the 1st law of thermodynamics, which provides

the expression for the energy conservation including both the mechanical energy

and the thermal energy.

From the kinetic theory of the ideal gas with the negligible intermolecular force,

the internal energy int of the gas with the temperature is given as follows:

int

(Eq. 2)

Here, the total number of molecules and the number of moles are related

by

(Eq. 3),

where × mol is called Avogadro‘s number. In addition,

Boltzmann constant × JK and the gas constant

Jmol⋅K from the ideal gas law are related

by

(Eq. 4).

Finally, the degree of freedom is given as follows:

Monatomic molecules :

Diatomic molecules :

※ Answer the following questions.

1. Investigate the equipartition of energy theorem involved in the degree

of freedom .

(2) Thermodynamic process

1) Isothermal process

For the isothermal process with the constant temperature, the expression for

the 1st law of thermodynamics is rewritten as follows:

ln

,

int

,

(Eq. 5)

2) Isovolumetric process

For the isovolumetric process with the constant volume, the expression for the

1st law of thermodynamics is rewritten as follows:

,

int

,

int (Eq. 6)

Here,

is called the molar specific heat at the constant volume.

3) Isobaric process

For the isobaric process with the constant pressure, the expression for the 1st

law of thermodynamics is rewritten as follows:

,

int

,

int (Eq. 7)

Here, is called the molar specific heat at the constant pressure.

Since the air consists mostly of diatomic molecules, the following results are

obtained.

,

(Eq. 8)

4) Adiabatic process

For the adiabatic process with no heat transfer, the expression for the 1st law

of thermodynamics is rewritten as follows:

,

int ,

int (Eq. 9)

(3) Heat engine

The heat engine is a device that does work by extracting the thermal energy

from the high-temperature heat reservoir and exhausting the thermal energy

to the low-temperature heat reservoir as shown Fig. 1. Since the work done

by the heat engine on its environment is , the thermal efficiency

of the heat engine is defined as the follows:

Student ID Name



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(Eq. 10)

Fig. 1. Structure of the heat engine.

Carnot engine operated by the reversible cycle consisting of isothermal and

adiabatic processes gives the maximum thermal efficiency.

※ Answer the following questions.

2. Show that Carnot engine gives the maximum thermal efficiency max

as follows:

max

(Eq. 11)

That is, the maximum thermal efficiency depends only on the temperature of

the high-temperature heat reservoir and the temperature of the

low-temperature heat reservoir .

In this experiment, the heat engine operated by the reversible cycle consisting

of isothermal and isobaric processes is used.

(i) In the initial part of the cycle, the air inside the cylinder is held at a constant

temperature due to the cold water. If a weight is placed on top of the piston,

the air is compressed so that the work is done on the gas and the heat is

exhausted to the cold water according to (Eq. 5).

(ii) In the second part of the cycle, the air inside the cylinder is held at a constant

pressure, but the heat reservoir is changed from the cold water to the hot water.

The heat is extracted from the hot water to the gas, causing the gas to be

expanded, shifting the piston up, and doing positive work according to (Eq. 7).

(iii) In the third part of the cycle, the air inside the cylinder is held at a constant

temperature due to the hot water. If a weight is lifted off the piston, the air

is expanded so that the work is done by the gas and the heat is extracted from

the hot water according to (Eq. 5).

(iv) In the final part of the cycle, the air inside the cylinder is held at a constant

pressure, but the heat reservoir is changed from the hot water to the cold water.

The heat is exhausted from the gas to the cold water, causing the gas to be

compressed, shifting the piston down, and doing negative work according to

(Eq. 7).



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3. Experimental Instruments

Items Quantity Usage Clean up method

Computer 1 set It is used to acquire and analyze data.It should be placed at the center of the

experiment table.

Computer interface 1 set It is used to convert analog signals to digital signals.It should be placed inside the basket of

the experiment table.

Computer interface

-to-power adaptor &

connection cable

1 ea. It is used to connect the computer interface to the wall power.It should be placed inside the basket of


USB cable 1 ea. It is used to connect the computer interface to the computer.It should be placed inside the basket of


Temperature sensor 2 ea.They are used to measure the temperatures of the hot and cold

waters.

They should be placed inside the basket

of the experiment table.

Pressure sensor 1 ea. It is used to measure the pressure of the air inside the cylinder.It should be placed inside the basket of




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Items Quantity Usage Clean up method

Rod stand 1 setThe heat engine and the rotary motion sensor are attached to the

rod stand.

It should be placed at the center of the

experiment table.

Heat engine 1 set It is used to measure the characteristics of the heat engine. It should be attached to the rod stand.

Slotted mass 1 ea.It is placed on top of the piston and provides the pressure to the

air inside the cylinder.It should be placed on top of the piston.

Drilled mass &

Mass hanger1 set It acts as a counterweight for the piston.

The string connecting the drilled mass

to the piston should be placed on the

rotary motion sensor‘s pulley.

Plastic container 2 ea. They act as the high & low-temperature heat reservoir, respectively.They should be placed at the center of


Rotary motion sensor 1 ea. It is used to measure the volume of the air inside the cylinder. It should be attached to the rod stand.

Water heater &

Water heater-to-power

connection cable

1 ea. It is used to prepare the hot water.It should be placed at the center of the

experiment table.

Thread 1 ea. It is used to connect the drilled mass to the piston.It should be placed inside the basket of

the common experiment table.

Paper towel 1 ea. It is used to remove water.It should be placed inside the basket of

the common experiment table.



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< How to Use the Computer Interface) >

[1] After confirming that the computer interface is off, use the computer

interface-to-power adaptor & connection cable to connect the computer

interface to the wall power and keep the computer interface off.

[2] Connect the sensors to the proper analog channels or digital channels and

use the USB cable to connect the computer interface to the computer. Note

that the connection among all experimental instruments should be completed

before the computer interface is turned on. Note that the computer interface

must not be damaged by connecting the computer interface to the computer

while the computer interface is on.

[3] After turning on the computer and the computer interface, open the

Capstone program. If the Capstone window appears, select “Tools → Hardware

Setup → Choose Interface → PASPORT or ScienceWorkshop 750”.

[4] Select the sensors at the positions in the screen that are equivalent to

the positions of the computer interface in the actual experiment by clicking.

[5] After selecting “Displays → Graph or Table” by double-clicking, show graphs

or tables on the screen.

[6] Click the “Record” button of the Capstone program to start the measurement

and check if the acquired data is displayed in the screen. After checking if

the zero status is displayed in the data, click the “Stop” button of the Capstone

program to stop the measurement.

[7] After completing the check of the zero status, click the “Record” button

of the Capstone program again to start the measurement. If the data is

acquired, click the “Stop” button of the Capstone program to stop the

measurement. Repeat this procedure to acquire the correct data.

[8] Save the data in the computer by selecting “File → Export Data → ******.txt”

in the menu of the Capstone program and copy the text files to a USB memory

prepared beforehand.

[9] After the experiment is finished, close the Capstone program and turn off

the computer interface and the computer. Clean up the experimental

instruments according to the suggested method.



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4. Experimental Procedures

(0) Setting before the experiment

1) Put the rod in the rod stand. Attach the heat engine to the rod by sliding

the heat engine’s rod clamp onto the rod. The heat engine should be oriented

with the piston end up and the heat engine should be positioned close to

the bottom of the rod stand.

2) Attach the rotary motion sensor to the top of the rod stand and align the

medium groove of the pulley of the rotary motion sensor so that a string coming

from the center of the heat engine’s piston platform will pass over the pulley.

3) Thread one end of a piece of string through the hole in the top of the piston

platform and tie that end of the string to the shaft of the piston under the

piston platform. Pass the other end of the string over the medium step of rotary

motion sensor’s pulley and attach the drilled mass & mass hanger totaling about

g . This mass acts as a counterweight for the piston.

4) Position the piston about or cm from the bottom of the cylinder and

attach the tube from the can to one port on the heat engine and attach the

tube from the pressure sensor to the other port on the heat engine.

5) Put the hot water prepared by the water heater into one of the plastic

containers. Put the cold water in the other plastic container. The large containers

keep the hot and cold temperatures constant during the heat engine cycle.

6) Place one temperature sensor in the hot water and place the other temperature

sensor in the cold water. Note that the temperature sensors are labeled hot

and cold in the software program so that you will have to pay attention to which

sensor you put in the hot water and which is in the cold water.

(1) Measurement of the diagram

1) After confirming that the computer interface is off, use the computer

interface-to-power adaptor & connection cable to connect the computer

interface to the wall power and keep the computer interface off.

2) Connect the pressure sensor to the analog channel A, the two temperature

sensors to the analog channel B and C, and the rotary motion sensor to the

digital channels 1 and 2 of the computer interface. Use the USB cable to connect

the computer interface to the computer.

3) After turning on the computer and the computer interface, open the Capstone

program. If the Capstone window appears, select “Tools → Hardware Setup →

Choose Interface → PASPORT or ScienceWorkshop 750”.

4) Select “Pressure Senor, Low”, “Temperature Sensor, Stainless Steel”, and “Rotary

Motion Sensor” at the positions in the screen that are equivalent to the positions

connected to the computer interface in the actual experiment by clicking.

5) After selecting “Displays → Digits” by double-clicking, show the Temperature

digits on the screen. After selecting “Displays → Graph” by double-clicking, show

the gauge pressure vs. the position of the piston graph on the screen.

6) Perform the following cycle without hesitating between steps. You may want

to practice a few times before recording a data run. Start with the can in the

cold water. This starting point will be called the state . Record the initial height

of the bottom of the piston. Click the “Record” button of the Capstone

program to start the measurement.

→ : Place the g mass on the piston platform.

→ : Move the can from the cold water to the hot water.

→ : Remove the g from the piston platform.

→ : Move the can from the hot water to the cold water.

7) Click the “Stop” button of the Capstone program to stop the measurement.

Save the data in the computer by selecting “File → Export Data → ******.txt”

in the menu of the Capstone program and copy the text files to a USB memory

prepared beforehand.

8) If the measurement is finished, close the Capstone program and turn off the

computer interface and the computer. Clean up the experimental instruments

according to the suggested method.

9) Draw the pressure vs. volume of the air graph by using a proper program.

We do not know the volume of the air directly, but we can calculate it by

measuring the volume of the can and adding the volume of the cylinder. We

will ignore the volume of the tubes.

can mm , can cm ,

cylinder mm , cylinder

can cylinder

× ×

m

Note that the height change cylinder of the cylinder is equal to

the position change of the piston. In addition, remember that

the (absolute) pressure is equal to the sum of the gauge pressure and the

atmospheric pressure × Pa .



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(2) Analysis of the diagram

1) Label the four corners of your graph as , , , and . Identify the

temperatures at states , , , and . Put arrows on the cycle to show the

direction of the process. Identify the types of processes (isothermal, etc.) and

the actual physical performance (put mass on, put in the hot water, etc.) for

→ , → , → , and → .

2) Calculate the maximum thermal efficiency max

of the heat engine

operating between the two temperatures and .

3) Identify and label the two processes in which heat is extracted from the

high-temperature heat reservoir. Calculate the heat extracted from the

high-temperature heat reservoir during the isobaric expansion (→) and the

isothermal expansion (→ ).

4) Identify and label the two processes in which heat is exhausted from the

low-temperature heat reservoir. Calculate the heat exhausted to the

low-temperature heat reservoir during the isobaric compression (→ ) and

the isothermal compression (→ ).

5) Calculate the thermal efficiency

and compare it with the

maximum thermal efficiency max .



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5. Experimental Values

(1) Measurement of the diagram & (2) Analysis of the diagram

StateTemperature

(K )

Initial height of the

cylinder (m )

Position of the

piston (m )

Volume (m )

×

×

Pressure

(Pa)

(JK )

Average value of

(JK )

Process Temperature (K ) (J)→

(isothermal compression) →average → ln

→

(isobaric expansion)→

→

(isothermal expansion) →average → ln

→

(isobaric compression)→

Thermal efficiency

of the heat engine

Maximum thermal efficiency Thermal efficiency max

× (%)

max

※ Note that → → and → → .



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StateTemperature

(K )


cylinder (m )

Position of the

piston (m )

Volume (m )

×

×

Pressure

(Pa)

(JK )

Average value of

(JK )



→


→


→


Thermal efficiency

of the heat engine


× (%)

max




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StateTemperature

(K )


cylinder (m )

Position of the

piston (m )

Volume (m )

×

×

Pressure

(Pa)

(JK )

Average value of

(JK )



→


→


→


Thermal efficiency

of the heat engine


× (%)

max




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6. Results and Discussions (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should

be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.)

※ Write down contents in terms of the following key points.

1. Confirm and according to Boyle’s law.

2. Confirm

and

according to Charles’ law.

3. From the area enclosed by the closed curve on diagram, calculate the net work done by the gas during the one cycle.



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7. Solution of Problems (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should

be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.)

8. Reference

Exp. #1-7 : Measurement of the Characteristics of the Heat...

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