Certainly! Let's convert the given temperatures to the required units step-by-step:
### i. Converting [tex]\(50^\circ C\)[/tex] to Fahrenheit
To convert Celsius ([tex]\(^\circ C\)[/tex]) to Fahrenheit ([tex]\(^\circ F\)[/tex]), we use the formula:
[tex]\[ F = C \times \frac{9}{5} + 32 \][/tex]
- Given [tex]\(C = 50^\circ C\)[/tex]:
[tex]\[ F = 50 \times \frac{9}{5} + 32 \][/tex]
First, compute:
[tex]\[ 50 \times \frac{9}{5} = 50 \times 1.8 = 90 \][/tex]
Then add 32:
[tex]\[ 90 + 32 = 122 \][/tex]
So,
[tex]\[ 50^\circ C = 122^\circ F \][/tex]
### ii. Converting [tex]\(27^\circ C\)[/tex] to Kelvin
To convert Celsius ([tex]\(^\circ C\)[/tex]) to Kelvin (K), we use the formula:
[tex]\[ K = C + 273.15 \][/tex]
- Given [tex]\(C = 27^\circ C\)[/tex]:
[tex]\[ K = 27 + 273.15 = 300.15 \][/tex]
So,
[tex]\[ 27^\circ C = 300.15 \, \text{K} \][/tex]
### iii. Converting 100 K to Celsius
To convert Kelvin (K) to Celsius ([tex]\(^\circ C\)[/tex]), we use the formula:
[tex]\[ C = K - 273.15 \][/tex]
- Given [tex]\(K = 100 \, \text{K}\)[/tex]:
[tex]\[ C = 100 - 273.15 = -173.15 \][/tex]
So,
[tex]\[ 100 \, \text{K} = -173.15^\circ C \][/tex]
In summary:
1. [tex]\( 50^\circ C = 122^\circ F \)[/tex]
2. [tex]\( 27^\circ C = 300.15 \, \text{K} \)[/tex]
3. [tex]\( 100 \, \text{K} = -173.15^\circ C \)[/tex]
