Converting temperature scales (Celsius scale Fahrenheit scale Kelvin scale)

9 Converting temperature scales (Celsius scale Fahrenheit scale Kelvin scale)

1. 50 ^oC = ….. ^oF ?

Solution

At standard atmospheric pressure, the freezing point of water is 0 ^oC on the Celsius scale and 32 ^oF on the Fahrenheit scale. At standard atmospheric pressure, the boiling point of water is 100 ^oC on the Celsius scale and 212 ^oF on the Fahrenheit scale.

0 ^oC = 32 ^oF and 100 ^oC = 212 ^oF. A change of 5 C^o = a change of 9 F^o.

For a Celsius scale, the distance between 0 ^oC and 100 ^oC divided into 100 equal intervals. For a Fahrenheit scale, the distance between 0 ^oC and 100 ^oC divided into 180 equal intervals.

T^oF = (180/100) T^oC + 32

T^oF = (9/5) T^oC + 32

T^oF = (9/5) 50 + 32

T^oF = (9) 10 + 32

T^oF = 90 + 32

T^oF = 122

50 ^oC = 122 ^oF

2. 86 ^oF = ….. ^oC ?

Solution

T^oC = (100/180)(T^oF – 32)

T^oC = (5/9)(T^oF – 32)

T^oC = (5/9)(86 – 32)

T^oC = (5/9)(54)

T^oC = (5)(6)

T^oC = 30

86 ^oF = 30 ^oC

3. 50^oC = ….. K ?

Solution

T = T ^oC + 273

T = 50 + 273

T = 323

50 ^oC = 323 K

4. 212^oF = ….. K ?

Solution

T^oC = (100/180)(T^oF – 32)

T^oC = (5/9)(T^oF – 32)

T^oC = (5/9)(212 – 32)

T^oC = (5/9)(180)

T^oC = (5)(20)

T^oC = 100

212 ^oF = 100 ^oC + 273

212 ^oF = 373 K

 

5. x ^oC = x ^oF

x = ….. ?

Solution

1 : Converting Celsius scale into Fahrenheit scale

2 : Converting Fahrenheit scale into Celsius scale

6. 122°F = ….. Celsius

Solution

The conversion between the two temperature scales can be written :

T_C = 5/9 (T_F – 32)

T_C = Temperature in Celsius, T_F = temperature in Fahrenheit

The temperature in Celsius :

T_C = 5/9 (122 – 32) = T_C = 5/9 (90) = 5 (10)

T_C = 50 ^oC

7. The figure below shows the temperature measurement of a liquid with the Fahrenheit scale thermometer! If the temperature of the liquid is measured using a Celsius scale thermometer, then what is the liquid temperature.

Known :

Fahrenheit scale (T_F) = 95^oF

Wanted : Celsius scale

Solution :

At a pressure of 1 atm, the freezing point of water is 0 °C while the Fahrenheit scale is 32 ^oF. Conversely, the boiling point of water for the Celsius scale is 100 ^oC while the Fahrenheit scale is 212 ^oF.

On the Celsius scale, between 0 °C and 100 ° C there are 100 ° while on the Fahrenheit scale between 32 °F to 212 °F there is 180°.

T_C = 100/180 (T_F – 32)

T_C = 5/9 (T_F – 32)

T_C = 5/9 (95 – 32)

T_C = 5/9 (63)

T_C = 315/9

T_C = 35^oC

8. Based on figure below, determine the temperature P on the Celsius thermometer.

Solution

T_C = 100/180 (T_F – 32)

T_C = 5/9 (T_F – 32)

T_C = 5/9 (104 – 32)

T_C = 5/9 (72)

T_C = 360/9

T_C = 40 ^oC

9. If the temperature of Celsius scale as shown in figure below, determine the temperature of Fahrenheit scale as shown in figure below.

Solution :

T^oF = (180/100) T^oC + 32

T^oF = (9/5) T^oC + 32

T^oF = (9/5) 60 + 32

T^oF = (9) 12 + 32

T^oF = 108 + 32

T^oF = 140

1. Converting temperature scales
2. Linear expansion
3. Area expansion
4. Volume expansion
5. Heat
6. Mechanical equivalent of heat
7. Specific heat and heat capacity
8. Latent heat, heat of fusion, heat of vaporization
9. Energy conservation for heat transfer