Question

Water equivalent of a body is measured in
A. kg
B. calorie
C. Kelvin
D. \[{m^3}\]

Answer 1

Hint: Use the relation of heat absorbed or evolved by a body of a given mass and specific heat through the given range of temperature.

Complete step by step solution:
Water equivalent of a body is defined as the mass of water which would absorb or evolve the same amount of heat as is done by the body in rising or falling through the same rise or fall in the temperature.
Let m= Mass of the body, c = Specific heat of the body, $\Delta \theta $ = rise in temperature
Then, heat given by the body \[\Delta Q = m \times c \times \Delta \theta \]
Let W be the water equivalent of the body. From definition, W gram of water also requires the same amount of heat to raise the temperature through$\Delta \theta $.

Let the same amount of heat be given to W grams of water and its temperature also rises by $\Delta \theta $. As the specific heat capacity of water is 1. Then, heat given to water is given by the equation
$Q = W \times 1 \times \Delta \theta $
Dividing both the equations, we get $W = mc$
Thus, the water equivalent of a body is numerically equal to the thermal capacity of the body.
So, the water equivalent of a body is measured in kilograms.

Hence, the correct option is (A).

Note: Water equivalent of a body is based on the principle of calorimetry that when two bodies at different temperatures are mixed, heat will be transferred from body at higher temperature to a body at lower temperature till both acquire the same temperature. Thermal capacity of a body and its water equivalent are numerically equal. If thermal capacity of a body is expressed in terms of mass of water, it is known as the water equivalent of the body.