If a thermometer is currently reading 42.5 °F, what is the temperature in Kelvin? Note: Tc = 5/9(TF – 32)
The Correct Answer and Explanation is:
To convert a temperature from Fahrenheit (°F) to Kelvin (K), we need to first convert the temperature to Celsius (°C) and then convert the Celsius value to Kelvin. The formulas for these conversions are as follows:
- Fahrenheit to Celsius:
Tc=59(TF−32)T_c = \frac{5}{9}(T_F – 32)Tc=95(TF−32)
where TFT_FTF is the temperature in Fahrenheit, and TcT_cTc is the temperature in Celsius. - Celsius to Kelvin:
TK=Tc+273.15T_K = T_c + 273.15TK=Tc+273.15
where TKT_KTK is the temperature in Kelvin, and TcT_cTc is the temperature in Celsius.
Now, let’s calculate the temperature in Kelvin for a thermometer reading of 42.5°F.
Step 1: Convert 42.5°F to Celsius
Using the formula:Tc=59(42.5−32)T_c = \frac{5}{9}(42.5 – 32)Tc=95(42.5−32)
First, subtract 32 from 42.5:42.5−32=10.542.5 – 32 = 10.542.5−32=10.5
Now, multiply by 59\frac{5}{9}95:Tc=59×10.5=5.8333… °CT_c = \frac{5}{9} \times 10.5 = 5.8333\ldots \, \text{°C}Tc=95×10.5=5.8333…°C
So, the temperature in Celsius is approximately 5.83 °C5.83 \, \text{°C}5.83°C.
Step 2: Convert Celsius to Kelvin
Now that we know the temperature in Celsius is approximately 5.83 °C5.83 \, \text{°C}5.83°C, we can convert it to Kelvin:TK=5.83+273.15=278.98 KT_K = 5.83 + 273.15 = 278.98 \, \text{K}TK=5.83+273.15=278.98K
Thus, the temperature is approximately 279 K.
Conclusion
So, the temperature of 42.5°F corresponds to 279 Kelvin.
