Question

$1kg$ of ice at $-{10}^{o}C$ is mixed with $4.4kg$ of water at ${30}^{o}C$. The final temperature of mixture is(specific heat of ice is $2100J/kgK$)

• A. ${2.3}^{o}C$
• B. ${4.4}^{o}C$
• C. ${5.3}^{o}C$
• D. ${8.7}^{o}C$

Answer 1

The correct option is D ${8.7}^{o}C$

Heat released by water to reach $0^{o}C$ is $Q_1=mc\Delta T=4.4\times 4200\times 30=55440J$

heat absorbed by ice to melt is $Q_2=2100\times 1\times 10+1\times 336\times {10}^3=347000J$

extra heat, $Q_1-Q_2=197400J$

$(m_1+m_2)C\Delta T=197400$

$\Rightarrow (T-0)=\frac{197400}{\left(\right(4.2+1)\times 4200)}$

so, $T={8.7}^{o}C$