Question

Please someone help me with this question ​

Answer 1

i) 104 °F

ii) 343 °K

Explanation:

We have the relationship between temperature in degrees Fahrenheit(y) and degrees Kelvin(x) as:

`y\:=\:(9)/(5)\left(x-273\right)+32`

i) When temperature in Kelvin is 313°K, the equivalent temperature in °F is:

`\begin{aligned}y &= (9)/(5)(313-273) + 32\\& = (9)/(5)(40) + 32\\&= 9 \cdot 8 + 32\\\\&= 72 + 32\\\\& = 104^\circ F\end{aligned}\\`

So at 313°K, the equivalent temperature is 104°F

`====================================`

ii) We are given the temperature in degrees Fahrenheit and asked to find the temperature in degrees Kelvin

We have the equation for temperature conversion from °K to °F as:

`y\:=\:(9)/(5)\left(x-273\right)+32`

Let's manipulate this equation so that x is given in terms of y

1. Switch sides:
   
   `(9)/(5)\left(x-273\right)+32 = y\\\\`
   
2. Subtract 32 from both sides
   
   `(9)/(5)\left(x-273\right)+32-32 = y-32\\\\`
   
3. Simplify
   
   `(9)/(5)\left(x-273\right) = y-32\\\\`
   
4. Multiply throughout by 5/9
   
   `(5)/(9) \cdot (9)/(5)\left(x-273\right) = (5)/(9) (y-32)\\\\`
   
5. 5/9 and 9/5 multiply to 1 giving
   
   `x - 273 = (5)/(9) (y-32)\\\\`
   
6. Add 273 to both sides, This cancels out 273 on the left
   
   `x = (5)/(9) (y-32) + 273\\`

Here x = degrees Kelvin and y = degrees Fahrenheit

Given y = 158°F, just plug in this value into the equation for x giving

`\begin{aligned}x &= (5)/(9)(158 - 32) + 273\\& = (5)/(9)(126) + 273\\&= 70 + 273\\&= 343\end{aligned}`

Therefore temperature in °K for temperature 158°F = 342 °K