Question

The specific heat of steel is $ 420J/(k{{g}^{0}}C) $ . How much energy is required to heat 1kg of steel by $ {{20}^{0}}C $ ?

Answer 1

Hint The answer is based on the concept of specific heat which tells about the amount of heat required in order to heat one unit of mass which is usually 1g of that substance by $ {{1}^{0}}C $ .

Complete step – by – step answer:
In the lower classes of physical chemistry, we have come across the concept of thermodynamics which includes the calculation of various parameters and also have come across the term specific heat.
Let us see what does specific heat mean and how can energy be calculated by using specific heat data.
- In chemistry, specific heat is given by the symbol $ 'c' $ and is defined as the ratio of heat capacity of a sample of the substance to that of mass of the sample.
- Now, in this case, by analyzing the data we can say that the specific heat of steel uses 1kg as the unit mass and this means that say ‘x’ amount of heat is required in order to heat 1kg of steel by $ {{1}^{0}}C $ .
It is given that specific heat capacity is $ c=420J/(k{{g}^{0}}C) $ and from this we can say that we need 420J of heat in order to increase the temperature of 1 kg of steel by $ {{1}^{0}}C $
Thus, in order to increase the temperature of steel by $ {{20}^{0}}C $ , we will need ‘x’ amount of heat and by the simple cross multiplication rule we have,
\[x={{20}^{0}}C\times \dfrac{420J}{1k{{g}^{0}}C}=8400Jk{{g}^{-1}}\]
Now, for 1kg the answer will be,
\[x=1kg\times 8400Jk{{g}^{-1}}=8400J\]

Hence, the correct answer is 8400J of heat is required to heat 1kg of steel by $ {{20}^{0}}C $

Note: Note that specific heat is an important quantity as it gives the indication of how much energy is required to heat or cool an object of given mass by a given amount, that is it indicates the ability of a substance to store heat.