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10-1.Thermometry, Thermal Expansion and Calorimetry
hard
$1\,\, kg$ of ice at $-10^o C$ is mixed with $4.4\,\, kg$ of water at $30^o C$. The final temperature of mixture is ........$^oC$ (specific heat of ice is $2100\,\,J/kg/k$)
A
$2.3$
B
$4.4$
C
$5.3$
D
$8.7$
Solution
Heat released by water to reach $0^{\circ} \mathrm{C}$ is $Q_{1}=m c \Delta T=4.4 \times 4200 \times 30=55440 \mathrm{J}$
heat absorbed by ice to melt is $Q_{2}=2100 \times 1 \times 10+1 \times 336 \times 10^{3}=347000 J$
extra heat, $Q_{1}-Q_{2}=197400 J$
$\left(m_{1}+m_{2}\right) C \Delta T=197400$
$\Rightarrow(T-0)=\frac{197400}{(4.2+1) \times 4200}$
so, $T=8.7^{\circ} \mathrm{C}$
Standard 11
Physics
