Embibe Experts Solutions for Chapter: Calorimetry and Thermal Expansion, Exercise 1: Exercise 1

How many grams of a liquid of specific heat $0.2 \mathrm{cal} {\mathrm{g}}^{-1} °{\mathrm{C}}^{-1}$ at a temperature of $40 °\mathrm{C}$ must be mixed with $100 \mathrm{gm}$ of a liquid of specific heat $0.5 \mathrm{cal} {\mathrm{g}}^{-1} °{\mathrm{C}}^{-1}$ at a temperature of $20 °\mathrm{C}$, so that the final temperature of the mixture becomes $32 °\mathrm{C}$.

$5 \mathrm{g}$ of ice at $0°\mathrm{C}$ is dropped in a beaker containing $20 \mathrm{g}$ of water at $40°\mathrm{C}$. The final temperature will be:

$50 \mathrm{gm}$ of ice at $0°\mathrm{C}$  is mixed with $50 \mathrm{gm}$ of water at $80°\mathrm{C}$, final temperature of mixture will be

(Latent heat of fusion of ice$=80 \mathrm{cal}/\mathrm{g}$, $s_w=1 \mathrm{cal}/\mathrm{g}°\mathrm{C}$)

$300 \mathrm{gm}$ of water at $25°\mathrm{C}$ is added to $100 \mathrm{gm}$ of ice at $0°\mathrm{C}$. The final temperature of the mixture is

Three liquids with masses $m_1, m_2, m_3$ are thoroughly mixed. If their specific heats are $c_1, c_2, c_3$ and their temperature $T_1, T_2, T_3$, respectively, then the temperature of the mixture is

A glass flask is filled up to a mark with $50 \mathrm{cc}$ of mercury at $18°\mathrm{C}$. If the flask and contents are heated to $38°\mathrm{C}$, how much mercury will be above the mark ? $\alpha$ for glass is $9\times {10}^{-6} {}^{\circ }\mathrm{C}^{-1}$ and coefficient of real expansion of mercury is $180\times {10}^{-6} {}^{\circ }\mathrm{C}^{-1}$.

A glass flask of volume one litre at $0°\mathrm{C}$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to $100°\mathrm{C}$. How much mercury will spill out, if the coefficient of volume expansion of mercury is $1.82\times {10}^{-4} {}^{\circ }\mathrm{C}^{-1}$ and linear expansion of glass is $0.1\times {10}^{-4} {}^{\circ }\mathrm{C}^{-1}$ respectively?

A piece of metal weighs $46 \mathrm{gm}$ in air. When it is immersed in the liquid of specific gravity $1.24$ at $27°\mathrm{C}$, it weighs $30 \mathrm{gm}$. When the temperature of the liquid is raised to $42°\mathrm{C}$ the metal piece weighs $30.5 \mathrm{gm}$, specific gravity of the liquid at $42°\mathrm{C}$ is $1.20$ , then the linear expansion of the metal will be: