Sure, I will walk you through the solution in detail.
(i) Find the temperature of the liquid in Fahrenheit (°F) if the temperature of the liquid is 513 K (Kelvin):
1. Convert Kelvin to Celsius:
The relationship between Kelvin and Celsius is given by the formula:
[tex]\[
C = K - 273.15
\][/tex]
where [tex]\( K \)[/tex] is the temperature in Kelvin and [tex]\( C \)[/tex] is the temperature in Celsius.
Given [tex]\( K = 513 \)[/tex]:
[tex]\[
C = 513 - 273.15 = 239.85 \, ^\circ C
\][/tex]
2. Convert Celsius to Fahrenheit:
The relationship between Celsius and Fahrenheit is given by the formula:
[tex]\[
F = \left(\frac{9}{5} \times C\right) + 32
\][/tex]
where [tex]\( F \)[/tex] is the temperature in Fahrenheit and [tex]\( C \)[/tex] is the temperature in Celsius.
Using [tex]\( C = 239.85 \)[/tex]:
[tex]\[
F = \left(\frac{9}{5} \times 239.85\right) + 32 = 431.73 + 32 = 463.73 \, ^\circ F
\][/tex]
Therefore, the temperature of the liquid in Fahrenheit is [tex]\( 463.73 \, ^\circ F \)[/tex].
(ii) Find the temperature of the liquid in Kelvin (K) if the temperature of the liquid is 158°F:
1. Convert Fahrenheit to Celsius:
The relationship between Fahrenheit and Celsius is given by the formula:
[tex]\[
C = \left(F - 32\right) \times \frac{5}{9}
\][/tex]
where [tex]\( F \)[/tex] is the temperature in Fahrenheit and [tex]\( C \)[/tex] is the temperature in Celsius.
Given [tex]\( F = 158 \)[/tex]:
[tex]\[
C = \left(158 - 32\right) \times \frac{5}{9} = 126 \times \frac{5}{9} = 70 \, ^\circ C
\][/tex]
2. Convert Celsius to Kelvin:
The relationship between Celsius and Kelvin is given by the formula:
[tex]\[
K = C + 273.15
\][/tex]
where [tex]\( C \)[/tex] is the temperature in Celsius and [tex]\( K \)[/tex] is the temperature in Kelvin.
Using [tex]\( C = 70 \)[/tex]:
[tex]\[
K = 70 + 273.15 = 343.15 \, K
\][/tex]
Therefore, the temperature of the liquid in Kelvin is [tex]\( 343.15 \, K \)[/tex].
These detailed steps should clarify how the temperature conversions are carried out effectively.
