Question

Convert the following temperatures to the Kelvin scale.
(a) $${25}^{\circ }C$$
(b) $${373}^{\circ }C$$

Answer 1

Hint:Water freezes at $$273.15\text{K}$$ and boils at $$373.15\text{K}$$. On the Celsius scale, water freezes at $$0^{\circ }C$$and boils at $${100}^{\circ }C$$. Therefore, we can say that $$273.15\text{K}$$ represents $$0^{\circ }C$$ on Celsius scale. Therefore, for each degree rise in temperature, there is a rise of 273 K in the Kelvin scale.

Formula used:
$$T_K=T_C^0+273.15$$
Here, $$T_K$$ is the temperature in Kelvin and $$T_C^0$$ is the temperature in Celsius.

Complete step by step solution:
We know that on the Kelvin scale, water freezes at $$273.15\text{K}$$ and boils at $$373.15\text{K}$$. On the Celsius scale, water freezes at $$0^{\circ }C$$and boils at $${100}^{\circ }C$$. Therefore, we can say that $$273.15\text{K}$$ represents $$0^{\circ }C$$ on Celsius scale.From the above discussion, we can write,
$$T_K=T_C^0+273.15$$
Here, $$T_K$$ is the temperature in Kelvin and $$T_C^0$$ is the temperature in Celsius.

(a) $${25}^{\circ }C$$
We can use the above formula to convert $${25}^{\circ }C$$ into Kelvin as follows,
$$T_K=T_C^0+273.15$$
Substituting $${25}^{\circ }C$$ for $$T_C^0$$ in the above equation, we get,
$$T_K=25+273.15$$
$$\therefore T_K=298.15\text{K}$$

Therefore, the temperature $${25}^{\circ }C$$ on the Kelvin scale is 298.15 K.

(b) $${373}^{\circ }C$$
We can use the above formula to convert $${373}^{\circ }C$$ into Kelvin as follows,
$$T_K=T_C^0+273.15$$
Substituting $${373}^{\circ }C$$ for $$T_C^0$$ in the above equation, we get,
$$T_K=373+273.15$$
$$\therefore T_K=646.15\text{K}$$

Therefore, the temperature $${373}^{\circ }C$$ on the Kelvin scale is 646.15 K.

Additional information:
The Kelvin temperature is never negative. You may wonder why Kelvin starts from 273.15 K and not from 0 K. The lowest temperature recorded on the earth is $$-{273.15}^{\circ }\text{C}$$. Since the Kelvin temperature cannot be negative, 273.15 K is added to$$-{273.15}^{\circ }\text{C}$$. Therefore, $${273.15}^{\circ }\text{C}+273.15\text{K}=0\text{K}$$. Therefore, the Kelvin always starts from 273.15 K to express the lowest temperature point on Celsius scale.

Note:Students must be aware not to confuse between the formula for converting Celsius temperature to Kelvin temperature and Celsius temperature to Fahrenheit temperature. You can avoid the number after the decimal to express the temperature in Kelvin scale. For example if the temperature is 273.15 K then you can write it as 273 K because figures after decimal point may create difficulties while doing calculations.