Question

A body of specific heat $0.2$ kcal$/k{g}^o$C is heated through ${100}^o$C. The percentage increase in its mass is?

• A. $9\%$
• B. $9.3\times {10}^{-11}\%$
• C. $10\%$
• D. None of these

Answer 1

The correct option is B $9.3\times {10}^{-11}\%$

From Einstein's mass energy relation
$E=\Delta m{c}^2$ .............(i)
where $\Delta$m is mass lost, c is speed of light. Also heat given by body is
$E=mC\Delta \theta$ ...........(ii)
where, C is specific heat.
Equating Eqs. (i) and (ii) we get
$\Delta m=\frac{MC\Delta \theta }{C^2}=\frac{M\times 0.2\times 100\times 4.2\times {10}^3}{(3\times {10}^8{)}^2}$
$\frac{\Delta m}{M}=\frac{20\times 4.2\times {10}^3}{(3\times {10}^8{)}^2}$
$\%$ increase in mass
$=\frac{\Delta m}{M}\times 100=\frac{20\times 4.2\times {10}^3}{(3\times {10}^8{)}^2}\times 100$
$=9.3\times {10}^{-11}\%$.