In the previous section we saw the details about the Celsius scale and the Fahrenheit scale to measure temperatures. In this section we will see another scale.
• Recall the rod in fig.6.4 on which various temperatures were marked.
• Now, a third group of scientists walk upto the rod and add some more details. The new details that they added are shown in magenta color in fig.6.14 below:
• We can see that, 273o K is marked at A. Also 373o K is marked at B. What do they mean?
• Ans: They have used a third scale. It is called the kelvin scale.
♦ In that scale, the heat content corresponding to the freezing point of water is given the value: 273.
♦ And the heat content corresponding to the boiling point of water is given the value 373.
• So this scale is similar to the Celsius scale. because, there are exactly 100 units between freezing point of water and boiling point of water.
• Because of this similarity in units, we can easily convert from Celsius to kelvin and vice versa. Let us see an example:
• The normal human body temperature is 37o C. Find how much it is in the kelvin scale?
Solution:
1. 37o C is 37 units above zero in the Celsius scale
2. The units in Celsius and Kelvin scales are of the same magnitude. Also, corresponding to zero in the Celsius scale, we have 273 in the kelvin scale.
3. So the required value is 37 units above 273 in the kelvin scale
4. Thus we have: 37o C = (273 + 37)o K = 310o K
From this problem, we get a general method:
• If C is the given temperature in the Celsius scale, and K is the required temperature in Kelvin scale, we can write:
Eq.6.4:
K = 273 + C
• This equation can be rearranged to obtain C, if we are given K. That is:
Eq.6.5:
C = K - 273
• Before we proceed to the next topic, we have to learn one more detail about the kelvin scale.
• In the fig.6.14, note the value of 0o K written at the left most end of the rod. It is a new point 'C'.
• According to the Kelvin scale, 0o K is the lowest possible temperature.
♦ At this temperature, the kinetic energy of the molecules become zero.
♦ This temperature is also called the absolute zero.
• Let us convert this absolute zero into Celsius scale:
1. From Eq.6.5, we have: C = K - 273.
2. The given temperature in K = absolute zero = 0o K
3. Substituting this in (1), we get: C = 0 - 273 = -273o C
• The precise value of absolute zero is -273.15o C
4. So the temperature in Celsius scale, corresponding to absolute zero is -273o C
• We can get a rough idea about 'how cold -273 C is' by considering the following facts:
♦ Carbon dioxide becomes solid to form dry ice at -78.5o C
♦ Oxygen turns from gaseous state to liquid state at -183o C
• Now let us see 'how much is absolute zero in the Fahrenheit scale':
1. We have: absolute zero = 0o K = -273.15o C
2. All we need to do is: Convert this C into F
We can use Eq.6.2:
F = [(9⁄5)×C + 32] =
We can add these details to fig.6.14 that we saw above. The modified fig.6.15 is shown below:
• Recall the rod in fig.6.4 on which various temperatures were marked.
• Now, a third group of scientists walk upto the rod and add some more details. The new details that they added are shown in magenta color in fig.6.14 below:
 |
| Fig.6.14 |
• Ans: They have used a third scale. It is called the kelvin scale.
♦ In that scale, the heat content corresponding to the freezing point of water is given the value: 273.
♦ And the heat content corresponding to the boiling point of water is given the value 373.
• So this scale is similar to the Celsius scale. because, there are exactly 100 units between freezing point of water and boiling point of water.
• Because of this similarity in units, we can easily convert from Celsius to kelvin and vice versa. Let us see an example:
• The normal human body temperature is 37o C. Find how much it is in the kelvin scale?
Solution:
1. 37o C is 37 units above zero in the Celsius scale
2. The units in Celsius and Kelvin scales are of the same magnitude. Also, corresponding to zero in the Celsius scale, we have 273 in the kelvin scale.
3. So the required value is 37 units above 273 in the kelvin scale
4. Thus we have: 37o C = (273 + 37)o K = 310o K
From this problem, we get a general method:
• If C is the given temperature in the Celsius scale, and K is the required temperature in Kelvin scale, we can write:
Eq.6.4:
K = 273 + C
• This equation can be rearranged to obtain C, if we are given K. That is:
Eq.6.5:
C = K - 273
• Before we proceed to the next topic, we have to learn one more detail about the kelvin scale.
• In the fig.6.14, note the value of 0o K written at the left most end of the rod. It is a new point 'C'.
• According to the Kelvin scale, 0o K is the lowest possible temperature.
♦ At this temperature, the kinetic energy of the molecules become zero.
♦ This temperature is also called the absolute zero.
• Let us convert this absolute zero into Celsius scale:
1. From Eq.6.5, we have: C = K - 273.
2. The given temperature in K = absolute zero = 0o K
3. Substituting this in (1), we get: C = 0 - 273 = -273o C
• The precise value of absolute zero is -273.15o C
4. So the temperature in Celsius scale, corresponding to absolute zero is -273o C
• We can get a rough idea about 'how cold -273 C is' by considering the following facts:
♦ Carbon dioxide becomes solid to form dry ice at -78.5o C
♦ Oxygen turns from gaseous state to liquid state at -183o C
• Now let us see 'how much is absolute zero in the Fahrenheit scale':
1. We have: absolute zero = 0o K = -273.15o C
2. All we need to do is: Convert this C into F
We can use Eq.6.2:
F = [(9⁄5)×C + 32] =
3. Substituting the given value of C, we get:
F = [(9⁄5)×(-273.15) + 32] = -491.67 + 32 = -459.67o FWe can add these details to fig.6.14 that we saw above. The modified fig.6.15 is shown below:
 |
| Fig.6.15 |
Solved example 6.3
What are the following temperatures in the Celsius scale?
(a) 491.67o F (b) 673 K
Solution:
In the next section, we will see Specific heat capacity.
What are the following temperatures in the Celsius scale?
(a) 491.67o F (b) 673 K
Solution:
Part 1:
1. In this problem, we have to convert from Fahrenheit to Celsius. We can use Eq.6.3:
1. In this problem, we have to convert from Fahrenheit to Celsius. We can use Eq.6.3:
C = (5⁄9)×[F-32]
2. Substituting the given value of F, we get:
C = (5⁄9)×[491.67-32] = (5⁄9)×[459.67] = 255.372o C
Part 2:
1. In this problem, we have to convert from Kelvin to Celsius. We can use Eq.6.5:
1. In this problem, we have to convert from Kelvin to Celsius. We can use Eq.6.5:
C = K - 273
2. Substituting the given value of K, we get:
C = 673 - 273 = 400o CIn the next section, we will see Specific heat capacity.
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