Question

The specific heat of water is $1cal{{g}^{-1}}{}^\circ {{C}^{-1}}$. Its SI units is approximately
A. 1
B. 4.2
C. 420
D.4200

Answer 1

Hint: Recall that the specific heat capacity is the amount of heat required to uniformly raise the temperature of a given sample by a small increment in temperature. So, we are supposed to find the amount of heat required to raise 1kg of water by 1K at particular temperature in SI units. As the value is given in another unit, you could simply convert it into the SI units to find the answer.

Complete step by step answer:
We have to find the approximate value of specific heat capacity of water in SI unit. Before that let us recall what the definition of heat capacity of a substance is.
Heat capacity of any substance may be defined as the amount of heat energy supplied in order to result in a unit change in temperature. This can be either increase or decrease of temperature, that is, it is the amount of heat energy required to result in rise or fall of temperature by 1℃. Normally, the heat capacity of a substance is expressed by s. We can express the heat capacity as,
$s=\dfrac{Q}{\Delta T}$
Where, Q is the heat supplied, ΔT is the temperature change.
But we are discussing specific heat capacity, which by the very name is a bit specific heat capacity. That is, the specific heat capacity of a substance is the amount of heat required by 1Kg of a substance to result in unit degree change (rise or fall) in temperature. It can be expressed as,
$C=\dfrac{Q}{m\Delta T}$
Where, Q is the heat supplied, ΔT is the resultant temperature change and m is the given amount of substance.
The SI unit of specific heat capacity is$Jk{{g}^{-1}}{{K}^{-1}}$.
Now that we know the SI unit of specific heat capacity, let us convert the given value to it.
From the question,
$C=1ca{{\lg }^{-1}}{}^\circ {{C}^{-1}}$
But we know that,
$1ca{{\lg }^{-1}}{}^\circ {{C}^{-1}}=4200Jk{{g}^{-1}}{{K}^{-1}}$
So the value of specific heat capacity of water in its SI units will be,$4200Jk{{g}^{-1}}{{K}^{-1}}$

So, the correct answer is “Option D”.

Note: We have to note here that the specific heat of a substance varies with temperature. Also, it is known to have different values for the same substance in its different states. For example, the specific heat capacity of water (liquid) and ice is very different. If the amount of substance was in moles, then, the heat capacity is molar specific whose SI unit is$Jmo{{l}^{-1}}{{K}^{-1}}$.