• We have seen that -273.15 oC corresponds to 0 K
• Based on that, we marked points B and C in fig.5.12
• For convenience, that fig.5.12 is shown again below:
 |
| Fig.5.12 |
• This fig.5.12 will help us to understand the basic features of the Kelvin scale. We will also see how to convert the readings from one scale to the other
• We can write them in 16 steps:
1. Six points are marked in the fig.5.12 They are: A, B, C, D, E and F
■ We already have the details about four points: A, B, C and E
Point A:
• Take a thermometer which is graduated in the Celsius scale
• Using that thermometer, measure the temperature of some water which is just at it’s freezing point
• The reading will be 0 oC
Point B:
• Take a thermometer which is graduated in the Celsius scale
• Using that thermometer, measure the temperature of a body which is at the lowest possible temperature
• The reading will be -273.15 oC
Point C:
• Take a thermometer which is graduated in the Kelvin scale
• Using that thermometer, measure the temperature of a body which is at the lowest possible temperature (The same body used for demonstrating point B)
• The reading will be 0 K
Point E:
• Take a thermometer which is graduated in the Celsius scale
• Using that thermometer, measure the temperature of some boiling water
• The reading will be 100 oC
2. We do not have the details about the remaining two points D and F
• To learn about those points, we first travel along the path: A-B-C-D
3. Imagine that, we are at A
(i) At A, we have a body at 0 oC
(ii) We reduce the ‘heat content’ of that body to such an extent that, it’s temperature becomes -273.15 oC
(iii) Thus we reach point B
4. The Celsius thermometer is first used at A and then at B
♦ When at A, the mercury reading is 0 oC
♦ When at B, the mercury falls below the 0 oC
(i) Mercury first falls through 273 equal divisions
(ii) Then it falls through 0.15 of one division
(iii) Thus we get a reading of -273.15 oC
5. Now we take the Kelvin thermometer
• When this thermometer is used at C, the reading is 0 K
• When this thermometer is used at D, the mercury rises
• How much does it rise?
The answer can be written in 5 steps:
(i) Size of divisions:
♦ The size of ‘one division’ in the Celsius scale
♦ is same as
♦ The size of one division in the Kelvin scale
(ii) Quantity of heat:
♦ The ‘heat lost’ from A to B
♦ is same as
♦ The 'heat gained' from C to D
(iii) So we have:
♦ Same sized divisions
♦ and
♦ Same heat content
(iv) As a consequence:
♦ Rise of mercury in Kelvin thermometer (when taken from C to D)
♦ will be same as
♦ Fall of mercury in Celsius thermometer (when taken from A to B)
(v) That means:
• When taken from C to D, the mercury will rise through 273.15 divisions in the kelvin thermometer
• So the reading will be 273.15 divisions above zero in the Kelvin thermometer
■ That is, the reading at D in the Kelvin thermometer will be 273.15 K
♦ So now we know the significance of point D
♦ It is the 'freezing point of water' in the Kelvin scale
6. Now we will see the remaining point F
• To learn about F, we first travel from A to E
♦ When at A, the mercury reading is 0 oC
♦ When at E, the mercury will rise through 100 divisions above 0 oC
7. Let us take the kelvin thermometer from D to F
♦ The size of divisions are the same
♦ The heat gained is also the same (that from A to E)
• So the mercury in the kelvin thermometer will also rise by 100 divisions
• This rise is from the '273 K reading' at D
■ So the reading at F will be 373 K
♦ So now we know the significance of point F
♦ It is the 'boiling point of water' in the Kelvin scale
■ Thus we have the details about all the points in fig.5.12
8. Next, we consider intermediate points in the fig.5.12
• Consider a point P in between A and B
♦ Since it is below 0, it will be a -ve reading
♦ Let the reading be -X
♦ It is shown in the fig.5.13(a) below:
 |
| Fig.5.13 |
• We want the corresponding reading in the kelvin thermometer
• It can be calculated in 3 steps:
(i) -X oC means that, the mercury falls by X divisions below 0 oC
(ii) So, in the Kelvin thermometer, the mercury will fall the same X divisions below 273.15 K
(iii) So the reading in the kelvin thermometer will be (273.15-X) K
9. Consider a point Q in between A and E
♦ Since it is above 0, it will be a +ve reading
♦ Let the reading be X oC
♦ It is shown in the fig.5.13(b) above
• We want the corresponding reading in the kelvin thermometer
• It can be calculated in 3 steps:
(i) +X oC means that, the mercury rises by X divisions above 0 oC
(ii) So, in the Kelvin thermometer, the mercury will rise the same X divisions above 273.15 K
(iii) So the reading in the kelvin thermometer will be (273.15+X)
10. Thus we have the method to convert from Celsius to kelvin scale. It can be written in 3 steps:
(i) The given Celsius reading may be +ve or -ve
(ii) Whatever be the sign, just 'add including the sign' to 273.15
(iii) The result will give the corresponding value in Kelvin scale
11. Next, we want to do the reverse. That is., we want to convert a given 'kelvin reading' into 'Celsius reading'
• For that, consider a point R in between C and D
♦ This is shown in fig.5.13(c) above
♦ Let the reading be Y K
♦ (Recall that, there will be no -ve readings in the Kelvin scale)
• Some heat will be lost while travelling from D to R
• How much heat is lost?
• The answer can be written in 4 steps:
(i) The distance from C to R is Y
(ii) The distance from C to D is 273.15
(iii) So the distance from D to R is: (273.15-Y)
(iv) This much heat is lost while travelling from D to Y
■ So the reading in the Celsius thermometer will be [0-(273.15-Y)] = [Y-273.15] c
■ This will be a negative value because, Y is less than 273.15 (R is between C and D)
12. Next, consider a point S between D and F
♦ This is shown in fig.5.13(d) above
♦ Let the reading be Y K
♦ (Recall that, there will be no -ve readings in the Kelvin scale)
• Some heat will be gained while travelling from D to Y
• How much heat is gained?
• The answer can be written in steps:
(i) The distance from C to S is Y
(ii) The distance from C to D is 273.15
(iii) So the distance from D to S is: (Y-273.15)
(iv) This much heat is gained while travelling from D to Y
■ So the reading in the Celsius thermometer will be [0+(Y-273.15)] = [Y-273.15] c
■ This will be a positive value because, Y is greater than 273.15 (S is between D and F)
13. Thus we have the method to convert from Kelvin to Celsius scale. It can be written in 3 steps:
(i) The given Kelvin reading will be always +ve
(ii) Subtract 273.15 from that given reading
(iii) The result will give the corresponding value in Celsius scale
14. The above results can be combined as follows:
■ To convert oC into K:
♦ K = 273.15 + C
♦ Some examples:
✰ 120 oC = (273.15 + 120) = 393.15 K
✰ -135 oC = (273.15 - 135) = 138.15 K
■To convert K into oC:
♦ C = K - 273.15
♦ Some examples:
✰ 320 K = (320 - 273.15) = 46.85 oC
✰ 142 K = (142 - 273.15) = -131.15 oC
15. We see that, the lowest possible temperature is 0 K
■ It is called: Absolute zero
16. Another name for Kelvin temperature scale is: Absolute temperature scale
• Yet another name for Kelvin temperature scale is: Thermodynamic scale
• This completes our present discussion on the basics of kelvin scale
Copyright©2020 Higher Secondary Chemistry. blogspot.in - All Rights Reserved
No comments:
Post a Comment