Question

Calculate the amount of heat required to convert 5 kg of ice at $0^{\circ }C$ to vapour at ${100}^{\circ }C$.

• A. $1.5\times {10}^{7}J$
• B. $2.5\times {10}^{7}J$
• C. $3.5\times {10}^{7}J$
• D. $4.5\times {10}^{7}J$

Answer 1

The correct option is A $1.5\times {10}^{7}J$

We have , $L_{ice}=3.34\times {10}^{5}J/kg,m=5kg$

From the definition of latent heat , heat required to convert ice into water at constant temperature $0^{o}C$ ,

$Q_1=m{L}_{ice}$

or $Q_1=5\times 3.34\times {10}^5=16.7\times {10}^{5}J$

Now , heat required to heat up the water at ${100}^{o}C$ from $0^{o}C$ ,

$Q_2=mc(100-0)=5\times 4200\times 100=21\times {10}^{5}J$ , where $c=4200J/kg{-}^{o}C$

Further ,$L_w=2.24\times {10}^{6}J/kg,m=5kg$

From the definition of latent heat , heat required to convert water into vapour at constant temperature ${100}^{o}C$ ,

$Q_3=m{L}_w$

or $Q_3=5\times 2.24\times {10}^6=112\times {10}^{5}J$

Total heat required ,

$Q=Q_1+Q_2+Q_3$

or $Q=16.7\times {10}^5+21\times {10}^5+112\times {10}^5=149.7\times {10}^5=1.5\times {10}^{7}J$