isothermal reversible ideal gas system the concepts deals with system in which the temperature of...

Isothermal reversible ideal gas system

The concepts deals with system in which the temperature of the system is constant

With the help of this animation user will be able to do expansion and contraction of the system at the constant temperature and check how does the isotherm is plotted

By Rachit AgarwalDepartment of chemistry

IIT Bombay

Instruction for user

temperature

pressure

volume

Master layout

Pressure tab

Temperature tab

volume tab Heat, change in enthalpy, work and change in internal energy displays

Up and down arrow key

Start and end button

Instruction box

piston weight System thermometer

Heat Q work WChange in enthalpy

Change in Internal energy

1) A constant temperature will be maintained during the process.

1) User can choose a temperature from the list given (this list will be shown in the instruction box)

1) User can change either volume or the pressure and other parameter pressure or volume respectively will be changed by following the law PV= NRT (N=1)

1) The parameter can by changed by using the down and up arrow tabs

1) Both the pressure and volume have their limit pressure 1 to 50 atm, volume from 1 to 50 lts

1) Start button – used to start the process

1) End button – used to stop the process

1) The graph should be plotted simultaneously once the user click the start button till the user presses the end button, even for the change in 0.5 units the graph should be plotted

Instructions for the animator: Working of the animation

select the temperature from the following 150k 300k 450k 600k

Instructions for the animator: Plotting of the graph

0 10 20 30 40 50

The x axis of the graph is the volume and the y axis of the graph is the pressure

Scale X axis 1 cm = 10 Lts of volumeY axis 1cm = 10 atms of pressure

EgFor P= 25 and V = 4The red dot shows the mark

For P = 2 and V = 50The blue dot shows the mark

And then both the line are joint by a curve line such that the P*V is constant i.e. for the above case P*V is 100 units, so the curve joining both the points should maintain the above relationship as shown in the graph by black curve

Definition and rules for the users

An isothermal is a process in which the temperature is maintained constant during the process, the graph of P v/s V is called as the isotherm at the constant temperature

The change in internal energy in isothermal process is zero (dU = nCvdT)work done is given by integral of –PdV ,

using the first law of thermodynamics the Q (heat) can be calculate as ∆u = Q + w , which implies the Q = -w as change in internal energy change for isothermal process is zero (dU = nCvdT)

the enthalpy can be calculated as H = U + PV , U and PV both are constant , therefore the change in enthalpy is zero for isothermal process

User will read the instruction in the instruction box and then follow the steps as said

It will choose a temperature at which the system process has to be carried

Then he will choose any of the two parameter i.e. pressure or volume and enter the initial value of one of the parameter, the value of the other parameter will come automatically by using the equation PV=nRT , here n =1 , both pressure and volume have limits of 1 to 50 units each

Then the user will click the start button and can change the selected parameter using the arrows tab and reach his final destination and then click the end button to stop the process and to get the values of work, heat, change in internal energy and change in enthalpy

Analogy / Scenario / Action / Example

Volume gradient: the size of the yellow box signifies the volume 100mm = 50lts and The size equal to 2mm = 1ltse.g. Initially yellow box (60mm in height) signifies the volume which is equivalent to 50 units, the finally yellow box (30mm in height) signifies the volume which is equivalent to 25 units

Pressure gradient: the color code (R:G:B 255:0:0) signifies the pressure equal to 1 atm and color code (R:G:B 0:0:0) signifies the pressure equal to 50 atme.g. initially red bar (255:0:0) signifies the pressure = 1atm and finally the bar (127:0:0) signifies pressure = 2 atm

Initial stage Final stage

Step 1 initial

Action Description Audio narration

enter temperature Allow the user to click the temperature tab

Please click the temperature tab

Circle the temperature tab Once the user clicks the temperature tab Make a yellow circle behind it

click the temperature tab

temperatureT

Step 1 final

enter temperature Allow the user to click the temperature tab

Please click the temperature tab

Circle the temperature tab Once the user clicks the temperature tab Make a yellow circle behind it

click the temperature tab

temperatureT

Step 2 initial

Temperature Allow the user to select the temperature from the list

Please select the temperature from the list in the instruction box

Circle the temperature selected Once the user select the temperature Make a yellow circle behind it and enter that particular value in the box above the temperature tab e.g. 300

select the temperature from the following 150K 300K 450K 600KInstruction for user

temperatureT

Step 2 final

Temperature Allow the user to select the temperature from the list

Please select the temperature from the list in the instruction box

Circle the temperature selected Once the user select the temperature Make a yellow circle behind it and enter that particular value in the box above the temperature tab e.g. 300

select the temperature from the following 150K 300K 450K 600K

temperatureT

Step 3 initial

Select the parameter Allow the user to click either on pressure or the volume tab

Please click the pressure or volume tab , the parameter you want to change

Circle the parameter selected Once the user select the pressure or the volume tab Make a yellow circle behind it E.g. case 1 pressureCase 2 volume

click on the one of the tab from pressure or volume that you want to change

temperatureT

pressure volume

Step 3.1 final

temperatureT

pressure volume

Case 1 Step 4.1 (pressure) initial

Actionz Description Audio narration

Using the up and down arrow key 1 atm should be displayed as default in pressure tabAllow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab

Range is from 1 atm to 50 atm with 0.5 atm as least count

Click start Allow the user to click the start button e.g the initial value set by the user is 5 atm

set the initial pressure from where you want to start the process using the down and up arrow key, range 1 atm to 50 atm with 0.5 atm as least count then click the start tab to start the process

temperatureT

pressureP

volumeV

Case 1 Step 4.1 (pressure) final

Using the up and down arrow key 1 atm should be displayed as default in pressure tabAllow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab

Range is from 1 atm to 50 atm with 0.5 atm as least count

Click start Allow the user to click the start button e.g the initial value set by the user is 5 atm

set the initial pressure from where you want to start the process using the down and up arrow key, range 1 atm to 50 atm with 0.5 atm as least count then click the start tab to start the process

temperatureT

pressureP

volumeV

Enter the value of the volume In the box above the volume tab enter the value calculated as (T*.0821/P) lts, in this case it is 4.926

The initial volume is (T*.0821/P) lts(speak the calculate vale) i.e. 4.962 lts

Change the height of yellow box and colour of piston (bar)

As the value of the of the pressure and the volume change the height of the yellow box and color of the piston (bar) changesThe gradient for the color and height is given by analogy slide

The volume is calculated using the equation PV= NRT

temperatureT

pressureP

volumeV

Enter the value of the volume In the box above the volume tab enter the value calculated as (T*.0821/P) lts, in this case it is 4.926

The initial volume is (T*.0821/P) lts(speak the calculate vale) i.e. 4.962 lts

The volume is calculated using the equation PV= NRT

temperatureT

pressureP

volumeV

4.926 lts

Draw the graph Plot the initial point on the graph , in this case at p= 5 and v = 4.962 by red dot

Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab. Eg shown for 0.5 atm change

Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over

Draw the graph Simultaneously draw the graph of P v/s V Eg shown for 0.5 atm change by blue dotDraw both the points with a black line

temperatureT

pressureP

volumeV

4.926 lts

Draw the graph Plot the initial point on the graph , in this case at p= 5 and v = 4.962 red dot

Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab. Eg shown for 0.5 atm change

Draw the graph Simultaneously draw the graph of P v/s V Eg shown for 0.5 atm change by blue dotDraw both the points with a black line

0 10 20 30 40 50

temperatureT

pressureP

volumeV

5.5 atm

4.478 lts

Action` Description Audio narration

Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab.

Value of volume The value of the volume will change every time the pressure is changedBy the formula (T*.0821/P) lts

Draw the graph Simultaneously draw the graph of P v/s V eg the end value reached by the user is P=50 atm then the value is shown by green dot , and a black line is drawn joining all the blue points that came by increment in 0.5atm

0 10 20 30 40 50

Your process has started, please change the value of pressure to change the state of the system then click the end button once the process is over

temperatureT

pressureP

volumeV

5.5 atm

4.478 lts

Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase pressure by 0.5 atm and on clicking the down arrow key decrease the pressure by 0.5 atm (do not across the range 1atm to 50 atm) , the value should change in the box above the pressure tab.

Value of volume The value of the volume will change every time the pressure is changedBy the formula (T*.0821/P) lts

Draw the graph Simultaneously draw the graph of P v/s V eg the end value reached by the user is P= 50 atm then the value is shown by green dot , and a black line is drawn joining all the blue points that came by increment in 0.5atm

0 10 20 30 40 50

Your process has started, please change the value of pressure to change the state of the system then click the end button once the process is over

temperatureT

pressureP

volumeV

50 atm

0.492 lts

Description Audio narration

End button Allow the user to click the end button when ever he wants to Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over

Value in boxes from heat and work tab

Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= -8.314*T*ln(Pi/Pf)) J , where Pi is the starting pressure and Pf is the final pressure. And heat as -W E.g. the final pressure by user is 25 atm then the work is =8028.52 J,And heat is -8028.5

Change in internal energy and change in internal energy will be zero because the process is isothermal, the work is (= -8.314*T*ln(Pi/Pf)) and heat is -W

0 10 20 30 40 50

temperatureT

pressureP

volumeV

50 atm

0.492 lts

End button Allow the user to click the end button when ever he wants to Your process has started, please change the value of pressure to change the state of the system and then click the end button once the process is over

Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= -8.314*T*ln(Pi/Pf)) J , where Pi is the starting pressure and Pf is the final pressure. And heat as -W E.g. the final pressure by user is 50 atm then the work is =9757.36 J,And heat is -9757.36 J

Change in internal energy and change in internal energy will be zero because the process is isothermal, the work is (= -8.314*T*ln(Pi/Pf)) and heat is -W

0 10 20 30 40 50

temperatureT

pressureP

volumeV

50 atm

0.492 lts

end Heat Q work WChange in enthalpy

0 J0 J-9757.36 J 9757.36 J

Step 3.2 final

temperatureT

pressure volume

Case 1 Step 4.2 (volume) initial

Using the up and down arrow key 1 lts should be displayed as default in volume tabAllow the user to click the up and down arrow keyOn click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the volume tab

Range is from 1 lts to 50 lts with 0.5 lts as least count

Click start Allow the user to click the start button e.g the initial value set by the user is 5 lts

set the initial volume from where you want to start the process using the down and up arrow key, range 1 lts to 50 lts with 0.5 lts as least count then enter the start tab to start the process

temperatureT

volumeV

pressureP

Case 1 Step 4.2 (volume) final

Using the up and down arrow key 1 lts should be displayed as default in volume tabAllow the user to click the up and down arrow keyOn click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the volume tab

Range is from 1 lts to 50 lts with 0.5 lts as least count

Click start Allow the user to click the start button e.g the initial value set by the user is 5 lts

set the initial volume from where you want to start the process using the down and up arrow key, range 1 lts to 50 lts with 0.5 lts as least count then enter the start tab to start the process

temperatureT

volumeV

pressureP

Enter the value of the pressure In the box above the pressure tab enter the value calculated as (T*.0821/V) atm, in this case it is 4.926 atm

The initial pressure is (T*.0821/V) atm(speak the calculate vale) i.e. 4.962 atm

The pressure is calculated using the equation PV= NRT

temperatureT

volumeV

pressureP

Enter the value of the pressure In the box above the pressure tab enter the value calculated as (T*.0821/V) atm, in this case it is 4.926 atm

The initial pressure is (T*.0821/V) atm(speak the calculate vale) i.e. 4.962 atm

The pressure is calculated using the equation PV= NRT

temperatureT

volumeV

pressureP

4.926 atm

Draw the graph Plot the initial point on the graph , in this case at v= 5 and p = 4.962 by red dot

Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the pressure tab. Eg shown for 0.5 lts change

Your process has started, please change the value of volume to change the state of the system and then click the end button once the process is over

Draw the graph Simultaneously draw the graph of P v/s V Eg shown for 0.5 lts change by blue dotDraw both the points with a black line

temperatureT

volumeV

pressureP

4.926 atm

0 10 20 30 40 50

Draw the graph Plot the initial point on the graph , in this case at v= 5 and p = 4.962 by red dot

Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase volume by 0.5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the pressure tab. Eg shown for 0.5 lts change

Draw the graph Simultaneously draw the graph of P v/s V Eg shown for 0.5 lts change by blue dotDraw both the points with a black line

temperatureT

volumeV

pressureP

5.5 lts

4.487 atm

Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase volume by .5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the volume tab.

Value of pressure The value of the pressure will change every time the volume is changedBy the formula (T*.0821/v) atm

Draw the graph Simultaneously draw the graph of P v/s V eg the end value reached by the user is v= 50 lts then the value is shown by green dot , and a black line is drawn joining all the blue points that came by increment in 0.5atm

0 10 20 30 40 50

Instruction for userYour process has started, please change the value of volume to change the state of the system and then click the end button once the process is over

temperatureT

volumeV

pressureP

5.5 lts

4.487 atm

0 10 20 30 40 50

temperatureT

volumeV

pressureP

50 lts

0.492 atm

Using the up and down arrow key Allow the user to click the up and down arrow keyOn click the up key increase volume by .5 lts and on clicking the down arrow key decrease the volume by 0.5 lts (do not across the range 1lts to 50 lts) , the value should change in the box above the volume tab.

Value of pressure The value of the pressure will change every time the volume is changedBy the formula (T*.0821/v) atm

Draw the graph Simultaneously draw the graph of P v/s V eg the end value reached by the user is v= 50 lts then the value is shown by green dot , and a black line is drawn joining all the blue points that came by increment in 0.5atm

Instruction for userYour process has started, please change the value of volume to change the state of the system and then click the end button once the process is over

0 10 20 30 40 50

temperatureT

volumeV

pressureP

50 lts

0.492 atm Instruction for userYour process has started, please change the value of volume to change the state of the system and then click the end button once the process is over

End button Allow the user to click the end button when ever he wants to Your process has started, please change the value of volume to change the state of the system you can also click on the pressure tab to change the pressure and then click the end button once the process is over

Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= -8.314*T*ln(Vf/Vi)) J , where Vi is the starting volume and Vf is the final volume. And heat as -W E.g. the final volume by user is 50 lts then the work is =-9757.36 J,And heat is 9757.36

0 10 20 30 40 50

temperatureT

volumeV

pressureP

50 lts

0.492 atm Instruction for userYour process has started, please change the value of volume to change the state of the system and then click the end button once the process is over

End button Allow the user to click the end button when ever he wants to Your process has started, please change the value of volume to change the state of the system you can also click on the pressure tab to change the pressure and then click the end button once the process is over

Enter the value in the enthalpy box as 0 J, internal energy as 0J and the value of work as (= -8.314*T*ln(Vf/Vi)) J , where Vi is the starting volume and Vf is the final volume. And heat as -W E.g. the final volume by user is 50 lts then the work is =-9757.36 J,And heat is 9757.36

Heat Q work WChange in enthalpy

0 J0 J9757.36 J - 9757.36 J

Links for further studies

References

books • PETER ATKINS , JULIO DE PAULA – PHYSICAL CHEMISTRY 8TH EDITION

• SIVA PLS ADD SOME BOOKS

Questionnaire

A system started at T=300K and pressure equal to 1atm ,

then the following steps were performed on the system isothermally , calculate the heat, work, change in internal energy, change in enthalpy in each case

Q1) volume is reduced to halfQ2) pressure is doubled Q3) volume is thricedQ4) pressure is taken to 5 atm

Answers

A1)a -1728.8,1728.8,0,0b 1728.8,-1728.8,0,0c -1728.8,-1728.8,0,0d 1728.8,1728.8,0,0

A2)a 1728.8,1728.8,0,0B -1728.8,1728.8,0,0c -1728.8,-1728.8,0,0d 1728.8,-1728.8,0,0

A3)a -2740.2,-2740.2,0,0b -2740.2,2740.2,0,0c 2740.2,-2740.2,0,0d 2740.2,2740.2,0,0

A4)a 4014.3,4014.3,0,0b 4014.3,-4014.3,0,0c -4014.3,-4014.3,0,0d -4014.3,4014.3,0,0

The order of the answer is as follows heat, work, change in internal energy, change in enthalpy in each case

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