Answer :
Sure, let's solve this step-by-step.
### Step 1: Convert from Celsius to Fahrenheit
We want to convert [tex]\( 25^\circ \text{C} \)[/tex] to Fahrenheit. The formula to convert from Celsius to Fahrenheit is:
[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.
Plugging in [tex]\( 25^\circ \text{C} \)[/tex]:
[tex]\[ F = \left(\frac{9}{5} \times 25\right) + 32 \][/tex]
[tex]\[ F = (45) + 32 \][/tex]
[tex]\[ F = 77^\circ \text{F} \][/tex]
### Step 2: Convert from Celsius to Kelvin
Next, we convert [tex]\( 25^\circ \text{C} \)[/tex] to Kelvin. The formula to convert from Celsius to Kelvin is:
[tex]\[ K = C + 273.15 \][/tex]
where [tex]\( K \)[/tex] is the temperature in Kelvin.
Plugging in [tex]\( 25^\circ \text{C} \)[/tex]:
[tex]\[ K = 25 + 273.15 \][/tex]
[tex]\[ K = 298.15 \text{ K} \][/tex]
### Conclusion
So, the temperatures in the respective scales are:
- [tex]\( 25^\circ \text{C} \)[/tex] is [tex]\( 77^\circ \text{F} \)[/tex] in Fahrenheit and [tex]\( 298.15 \text{ K} \)[/tex] in Kelvin.
From the given options:
- (e) [tex]\( 25^{\circ} C : 77^{\circ} F \)[/tex] and [tex]\( 298 \text{ K} \)[/tex] is the correct match.
Thus, the correct answer is:
[tex]\[ \boxed{e} \][/tex]
### Step 1: Convert from Celsius to Fahrenheit
We want to convert [tex]\( 25^\circ \text{C} \)[/tex] to Fahrenheit. The formula to convert from Celsius to Fahrenheit is:
[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.
Plugging in [tex]\( 25^\circ \text{C} \)[/tex]:
[tex]\[ F = \left(\frac{9}{5} \times 25\right) + 32 \][/tex]
[tex]\[ F = (45) + 32 \][/tex]
[tex]\[ F = 77^\circ \text{F} \][/tex]
### Step 2: Convert from Celsius to Kelvin
Next, we convert [tex]\( 25^\circ \text{C} \)[/tex] to Kelvin. The formula to convert from Celsius to Kelvin is:
[tex]\[ K = C + 273.15 \][/tex]
where [tex]\( K \)[/tex] is the temperature in Kelvin.
Plugging in [tex]\( 25^\circ \text{C} \)[/tex]:
[tex]\[ K = 25 + 273.15 \][/tex]
[tex]\[ K = 298.15 \text{ K} \][/tex]
### Conclusion
So, the temperatures in the respective scales are:
- [tex]\( 25^\circ \text{C} \)[/tex] is [tex]\( 77^\circ \text{F} \)[/tex] in Fahrenheit and [tex]\( 298.15 \text{ K} \)[/tex] in Kelvin.
From the given options:
- (e) [tex]\( 25^{\circ} C : 77^{\circ} F \)[/tex] and [tex]\( 298 \text{ K} \)[/tex] is the correct match.
Thus, the correct answer is:
[tex]\[ \boxed{e} \][/tex]
