Question

The specific heat capacity of water is
A. $4.2J/kg/{}^oC$
B. $4200J/kg/{}^oC$
C. $2.4J/kg/{}^oC$
D. $2400J/kg/{}^oC$

Answer 1

Hint: The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of one kilogram of the substance by ${1^o}C$ or $1K$ . In other words, it is the amount of heat energy required to one unit mass of a substance to raise its temperature by one unit.

Complete step by step answer:

The specific heat of water is the amount of heat energy required to raise the temperature of 1 kilogram of water by ${1^o}C$ or $1K$. The mathematical formula of specific heat capacity of any substance can be written as:
$Q = m \times c \times \Delta T$ …..(i)
Where, $Q = $ Heat energy required
$m = $ mass of the substance whose temperature needs to be raised
$c = $ specific heat capacity of the substance which varies for different substances
$\Delta T = $ rise in temperature or simply, change in temperature
The specific heat capacity of water can be determined using the formula mentioned above. The S.I unit of heat is calorie. The relation between joule and calorie is as follows:
$1calorie = 4.2J$ …..(ii)
As we are calculating the specific heat capacity of water, we will take the mass of water to be heated as one kilogram and the rise in temperature to be one degree celcius or one Kelvin.
Thus, $c = \dfrac{Q}{{m \times \Delta T}}$
$c = \dfrac{{1cal}}{{1kg \times {1^o}C}}$ …(iii)
But, according to the options provided above, there is a need to change the unit of the heat from calorie to joule. Hence, applying equation (ii) in equation (iii), we have:
$c = \dfrac{{4.2J}}{{1kg \times {1^o}C}} = 4.2J/kg{/^o}C$
Hence, the correct option is A. $4.2J/kg/{}^oC$ .

Note:
The specific heat generally varies with temperature and is different for each state of matter. Liquid water has one of the highest specific heats among the available common substances. The specific heat of a substance, especially a gas, may be significantly higher when it is allowed to expand as it is heated (specific heat at constant pressure) than when it is heated in a closed vessel that prevents expansion (specific heat at constant volume).