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# Write the approximate value of specific heat capacity of water in the SI unit.A. $420Jk{{g}^{-1}}{{K}^{-1}}$ B. $400Jk{{g}^{-1}}{{K}^{-1}}$ C. $2100Jk{{g}^{-1}}{{K}^{-1}}$ D. $4200Jk{{g}^{-1}}{{K}^{-1}}$

Last updated date: 16th Sep 2024
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Hint: We know 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. Also, remember that the specific heat capacity may vary with temperature. So, we are supposed to find the amount of heat required to raise 1kg of water by 1K at a particular temperature and also find value in the SI unit.

We are asked to find the approximate value of specific heat capacity of water in the SI unit. Before that let us recall what heat capacity of a substance is.
Heat capacity of a substance can be defined as the amount of heat energy supplied in order to result in a unit change in temperature. This change can be either increase or decrease, 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.
In case of specific heat capacity (C) the amount of substance is specified. 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$Jk{{g}^{-1}}{{K}^{-1}}$.
It is important to note here that the specific heat of a substance often varies with temperature. Also, it has different values for the same substance in its different states. For example, the specific heat capacity of water (liquid) and ice is different.
For a temperature of about 25℃ the heat required to raise the temperature of 1kg of water by 1K is 4179.6 joules, that is, the specific heat capacity of water in SI unit can be given by, $4179.6Jk{{g}^{-1}}{{K}^{-1}}$ .
${{C}_{water}}\approx 4200Jk{{g}^{-1}}{{K}^{-1}}$

So, the correct answer is “Option D”.

Note: If the amount of substance was in moles, the, the heat capacity is molar specific whose SI unit is $Jmo{{l}^{-1}}{{K}^{-1}}$. Instead if the amount was expressed in volume of the substance then the specific heat is volumetric whose SI unit is $J{{m}^{-3}}{{K}^{-1}}$. We also have specific heats at constant pressure and constant volume which is expressed as ${{C}_{P}}$, ${{C}_{V}}$ respectively.