Question

The specific heat capacity of water is $4200Jk{g^{ - 1}}{K^{ - 1}}$ .
(A) True
(B) False

Answer 1

Hint : The specific heat capacity of a substance is defined as the heat energy required to raise the temperature of unit mass of the substance by $1^\circ C$ . The term was initially defined such that the specific heat capacity of water would be $1$ , this resulted in a unit of energy known as calorie.

Complete step by step answer
The term specific heat capacity was defined to determine the amount of heat required to raise the temperature of a unit mass of the water by $1^\circ C$ . Since water is the most commonly used liquid in calorimetry, a new unit of energy was defined, it was called ‘calorie’.
A calorie is defined as the amount of heat required to raise the temperature of $1$ gram of water by
$\Rightarrow 1^\circ C$ . According to this the specific heat capacity of water is $1cal{\text{ }}{{\text{g}}^{ - 1}}^\circ {C^{ - 1}}$ .
The dimensions (units) used in this value and the units given in the question are different.
The question uses the SI system (metric system) to define the specific heat capacity of water.
So, on converting each dimension to the SI units, we get-
Mass- We know that, $1$ kilogram is equal to $1000$ grams, the term can be written as-
$\Rightarrow \eta = 1 \times 1000{\text{ }}cal{\text{ k}}{{\text{g}}^{ - 1}}^\circ {C^{ - 1}}$
$\Rightarrow \eta = 1000{\text{ }}cal{\text{ k}}{{\text{g}}^{ - 1}}^\circ {C^{ - 1}}$
Temperature- Kelvin is the SI unit for temperature, the relationship between Celsius and kelvin is linear which means, to convert Celsius into kelvin we only add a constant number, which is $273$ . Any quantity that contains a dimension of temperature difference, is same whether it is written in kelvin or in Celsius. Therefore the term remains-
$\Rightarrow \eta = 1000{\text{ }}cal{\text{ k}}{{\text{g}}^{ - 1}}{K^{ - 1}}$
Energy- Joule is the SI unit of energy and is defined in metric terms, in joules a calorie is related as-
$\Rightarrow 1cal = 4.2J$ (Approximately)
Applying this to the given term-
$\Rightarrow \eta = 4.2 \times 1000{\text{ J k}}{{\text{g}}^{ - 1}}{K^{ - 1}}$
$\therefore \eta = 4200{\text{ J k}}{{\text{g}}^{ - 1}}{K^{ - 1}}$
This matches the term given in the question, therefore the statement is true.

Note
The term calorie was defined specifically keeping the properties of water in mind, therefore most of the times the values corresponding to water in calories are unity. The joules, on the other hand, is derived from other metric units, and therefore has to be equated with calories to find the equivalent value.