10 g of ice at 0^∘ C is mixed with 100 g of water at 50^∘ C in a calorimeter. The final temper

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10 g of ice at 0^∘ C is mixed with 100 g of water at 50^∘...

$10 \mathrm{~g}$ of ice at $0^{\circ} \mathrm{C}$ is mixed with $100 \mathrm{~g}$ of water at $50^{\circ} \mathrm{C}$ in a calorimeter. The final temperature of the mixture is [Specific heat of water $=1$ cal $\mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1}$, latent heat of fusion of $\left.\mathrm{ice}=80 \mathrm{cal} \mathrm{g}^{-1}\right]$ (a) 31. $2^{\circ} \mathrm{C}$ (b) $32.8^{\circ} \mathrm{C}$ (c) $36.7^{\circ} \mathrm{C}$ (d) $38.2^{\circ} \mathrm{C}$

$10 \mathrm{~g}$ of ice at $0^{\circ} \mathrm{C}$ is mixed with $100 \mathrm{~g}$ of water at $50^{\circ} \mathrm{C}$ in a calorimeter. The final temperature of the mixture is [Specific heat of water $=1$ cal $\mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1}$, latent heat of fusion of $\left.\mathrm{ice}=80 \mathrm{cal} \mathrm{g}^{-1}\right]$
(a) 31. $2^{\circ} \mathrm{C}$
(b) $32.8^{\circ} \mathrm{C}$
(c) $36.7^{\circ} \mathrm{C}$
(d) $38.2^{\circ} \mathrm{C}$

Key Concepts

Thermal Equilibrium

Thermal equilibrium is the condition reached when two or more substances in contact with each other no longer exchange heat, resulting in a uniform temperature throughout the system. This concept is essential in calorimetry, as it signifies the final state where all energy transfers have balanced out.

Specific Heat Capacity

Specific heat capacity is the property of a material that quantifies the amount of heat energy required to raise the temperature of one gram of the substance by one degree Celsius. This concept is fundamental in calculating the energy changes involved in temperature changes when no phase transitions occur.

Latent Heat of Fusion

Latent heat of fusion is the amount of energy required to convert a substance from a solid phase to a liquid phase at its melting point without changing its temperature. It plays a critical role in scenarios where a phase change occurs, as the energy absorbed during the melting process must be accounted for separately from the energy used in increasing temperature.

Calorimetry

Calorimetry is the study of heat transfer between substances, typically involving calculations where heat lost by a warmer substance is equal to heat gained by a cooler one, assuming no heat loss to the surroundings. It provides the framework for solving problems involving mixing substances at different temperatures until thermal equilibrium is reached.

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