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 range of temperature. It is represented by W. It is the quantity of water whose thermal capacity is same as the heat capacity of the body.
ΔQ = mcΔθ … (1)
m = Mass of the body,
c = Specific heat of body,
Δθ = Rise in temperature.
If same amount of heat is given to W gram of water and its temperature also rises by Δθ. Then:
Heat given to water (Q) = W x 1 x Δθ … (ii)
From equations (i) and (ii): ΔQ = mcΔθ = W x 1 x Δθ.
Water equivalent (W) = mc gm
The product of the mass of a substance by its specific heat equal numerically to the mass of water that is equivalent in thermal capacity to the substance is known as water equivalent of that substance.
The SI unit of Water equivalent is Kg and the dimensional formula is [M¹L⁰T⁰]. Thermal capacity of the body and its water equivalent are numerically equal. If thermal capacity of a body is expressed in terms of mass of water it is called as Water Equivalent of the body.
The water equivalent of a substance is numerically equal to that heat capacity of a substance in CGS system but no dimensionally.