Question

The water equivalent of $20\text{g}$ of aluminium (specific heat $0.2{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$) , is

• A. $40\text{g}$
• B. $4\text{g}$
• C. $8\text{g}$
• D. $160\text{g}$

Answer 1

The correct option is B $4\text{g}$

Given
Mass of aluminium $\left(m_a\right)=20\text{g}$
Specific heat of aluminium $\left(c_a\right)=0.2{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$

Water equivalent of a body is defined as the mass of water which would absorb or release the same amount of heat as the body in rising or falling through the same range of temperature.
Heat given to aluminium $\left(H_a\right)=m_a\times c_a\times \Delta T....\left(1\right)$
Heat given to water $\left(H_w\right)=m_w\times c_w\times \Delta T.....\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$, we get
Water equivalent $\left(m_w\right)=\frac{m_a{c}_a}{c_w}$
We know that,specific heat capacity of water $\left(c_w\right)=1{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$
Hence, water equivalent $\left(m_w\right)=\frac{20\times 0.2}{1}=4\text{g}$
Thus, option (b) is the correct answer.