Question

Find the increase in mass when 1 kg of water is heated from 0${}^o$C to ${100}^o$C. Specific heat capacity of water = 4200 J kg${}^{-1}$ K${}^{-1}$

• A. $9.7\times {10}^{-12}kg$
• B. $8.7\times {10}^{-12}kg$
• C. $4.7\times {10}^{-12}kg$
• D. $14.7\times {10}^{-12}kg$

Answer 1

The correct option is C $4.7\times {10}^{-12}kg$

Given : $\Delta T=100-0={100}^{o}C$ $m_o=1$kg $S=4200$ $J/kg.K$

Thus amount of heat required to raise the temperature $Q=mS\left(\Delta T\right)=1\times 4200\times 100=4.2\times {10}^5$ $J$

Using Einstein's mass-energy equivalence, $E=m{c}^2$ where $m$ is the increase in mass

$\therefore$ $4.2\times {10}^5=m\times (3\times {10}^8{)}^2$ $⟹m=4.7\times {10}^{-12}$ kg