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Heat energy of 184 \mathrm{~kJ} is given to ice of mass 600 \mathrm{~g} at -12^{\circ} \mathrm{C}. Specific heat of ice is 2222.3 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{C}^{-1} and latent heat of ice in 336 \mathrm{kJkg}^{-1}
A. Final temperature of system will be 0^{\circ} \mathrm{C}.
B. Final temperature of the system will be greater than 0^{\circ} \mathrm{C}.
C. The final system will have a mixture of ice and water in the ratio of 5: 1.
D. The final system will have a mixture of ice and water in the ratio of 1: 5.
E. The final system will have water only.
Choose the correct answer from the options given below:

Option: 1

A and D Only


Option: 2

A and E Only


Option: 3

A and C Only


Option: 4

B and D Only


Answers (1)

best_answer

Heat energy given =184 \mathrm{KJ}=184 \times 10^3 \mathrm{~J}
Amount of heat required to raise the temperature
$$ \begin{aligned} \theta_1=\mathrm{ms}_{\mathrm{ice}} \Delta \mathrm{T} & =0.6 \times 2222.3 \times 12 \\ & =16000.56 \mathrm{~J} \end{aligned}
Remaining heat \theta_2=184000-16000.56=167999.44 \mathrm{~J}
For melting at 0^{\circ} \mathrm{C} heat required =\mathrm{mL}_{\mathrm{f}}
$$ \begin{aligned} & =0.6 \times 336000 \\ & =(201600) \mathrm{J} \text { needed } \end{aligned}
\therefore 100 \%  ice is not melted
Amount of ice melted
$$ 167999.44=\mathrm{m} \times 336000
\mathrm{m}= mass of water =0.4999 \mathrm{Kg}
Mass of ice =0.1001
$$ \text { Ratio }=\frac{0.1001}{0.4999} \approx 1: 5

Posted by

Divya Prakash Singh

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