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प्रश्न
If the temperature of a liquid can be measured in Kelvin units as x°K or in Fahrenheit units as y°F, the relation between the two systems of measurement of temperature is given by the linear equation
`y = 9/5 (x - 273) + 32`
- Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313°K.
- If the temperature is 158°F, then find the temperature in Kelvin.
उत्तर
Given relation is `y = 9/5 (x - 273) + 32` ...(i)
i. Given, x = 313°K, then from equation (i), we get
`y = 9/5 (313 - 273) + 32`
= `9/5 xx 40 + 32`
= 9 × 8 + 32
= 72 + 32
= 104°F
ii. Given, y = 158°F, then from equation (i), we get
`158 = 9/5 (x - 273) + 32`
⇒ `158 = (9(x - 273) + 32 xx 5)/5`
⇒ 158 × 5 = 9(x – 273) + 160
⇒ 790 = 9(x – 273) + 160
⇒ 790 – 160 = 9(x – 273)
⇒ 9(x – 273) = 630
⇒ `x - 273 = 630/9 = 70`
⇒ x – 273 = 70
∵ x = 70 + 273 = 343°K
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