If the temperature of a liquid can be measured in Kelvin units as x K and in Fahrenheit units as y °F, the relation between the two systems of measurement of temperature is given by the linear equation y = 95(x − 273) + 32.
- (i) Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313 K.
- (ii) If the temperature is 158 °F, then find the temperature in Kelvin.
Answer: (i) 313 K = 104 °F (ii) 158 °F = 343 K.
Step-by-step solution
Given: y = 95(x − 273) + 32, where x is in K and y in °F
Idea: (i) gives x, so substitute and work out y. (ii) gives y, so substitute and solve the linear equation for x.
(i) Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313 K.
- x = 313: y = 95(313 − 273) + 32 = 95 × 40 + 32½ mark
- = 72 + 32 = 104 °F.1 mark
104 °F
(ii) If the temperature is 158 °F, then find the temperature in Kelvin.
- y = 158: 158 = 95(x − 273) + 32 ⇒ 95(x − 273) = 126.½ mark
- x − 273 = 126 × 59 = 70 ⇒ x = 343 K.1 mark
343 K
(i) 104 °F (ii) 343 K
Check: (ii) back in the formula: 95(343 − 273) + 32 = 95 × 70 + 32 = 126 + 32 = 158 ✓.
Answer to write in the exam
(i)
y = 95(313 − 273) + 32
= 95 × 40 + 32 = 72 + 32
∴ Temperature = 104 °F
(ii)
158 = 95(x − 273) + 32
95(x − 273) = 126
x − 273 = 126 × 59 = 70
∴ Temperature = 343 K
Common mistakes that cost marks
- Working out 95 × 313 − 273 instead of 95 × (313 − 273). Do the bracket first.
- In (ii), forgetting to subtract 32 before dividing by 95.
- Multiplying by 95 instead of 59 when undoing the 95 in (ii).
How this can come in the exam
MCQ (1 mark)
Using y = 95(x − 273) + 32, the temperature 273 K in °F is
- 0 °F
- 32 °F
- 273 °F
- 212 °F
Show answer
(B) 32 °F
95 × 0 + 32 = 32 °F (the melting point of ice).
Short answer (2 marks)
Using the same relation, convert 212 °F into kelvin.
Show answer
95(x − 273) = 180 (1 mark) ⇒ x − 273 = 100 ⇒ x = 373 K (1 mark).Try one yourself
Using y = 95(x − 273) + 32, convert 298 K into °F.
Show answer
95 × 25 + 32 = 45 + 32 = 77 °F.
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