Question

SI unit of water equivalent of the calorimeter is
(A) $Kg$
(B) $K{g}^3$
(C) $K{g}^2$
(D) $K{g}^{-1}$

Answer 1

Hint: Water equivalent is nothing but the amount of water that would absorb the same amount of heat as the calorimeter per degree temperature increase. A calorimeter is used to measure the heat flow. With the data provided, we can determine the specific heat capacity as well as the latent heat of phase transition.

Complete step by step solution:
The water equivalent is represented by $W$. It is the quantity of water in which thermal capacity is the same as the heat capacity of the body.
$\mathrm{\Delta }Q=mc\mathrm{\Delta }\theta ......................\left(1\right)$
Where,
$m$ is the mass of the body
$c$ is the specific heat of the body
$\mathrm{\Delta }\theta$ rise in temperature
If the same amount of heat is given to the $W$ gram of water and its temperature rises by $\mathrm{\Delta }\theta$.
Then,
Heat given to the water, $Q=W\times 1\times \mathrm{\Delta }\theta ..................\left(2\right)$
From equation (1) and (2),
$\mathrm{\Delta }Q=mc\mathrm{\Delta }\theta =W\times 1\times \mathrm{\Delta }\theta$
Water equivalent, $W=mc$
The product of a mass of the substance by its specific heat equal numerically to the mass of the water that is equivalent in thermal capacity to that substance is known as water equivalence of that substance.
The SI unit for water equivalence is $Kg$ and its dimensional formula is $M^1{L}^0{T}^0$. The thermal capacity of the body and its water equivalent are numerically equal. If the thermal capacity of the body is expressed in terms of the mass of water then it is called Water equivalence of the body.

$\therefore$ The SI unit of water equivalent of the calorimeter is $Kg$. Hence the option (A) is correct.

Note:
The specific heat of the water is $1cal.g^{-1}$ which means that $1cal$ heat will raise the temperature of $1g$ water by $1^{\circ }C$. The water equivalent of the substance is numerically equal to the heat capacity of the substance in the CGS system but not dimensionally.