Embibe Experts Solutions for Chapter: Thermal Properties of Matter, Exercise 1: WBJEE 2019

A horizontal fire hose with a nozzle of cross-sectional area $\frac{5}{\sqrt{21}}\times {10}^{-3} {\mathrm{m}}^2$ delivers a cubic metre of water in $10 \mathrm{s}.$ What will be the maximum possible increase in the temperature of water while it hits a rigid wall (neglecting the effect of gravity)?

When $100 \mathrm{g}$ of boiling water at $100°\mathrm{C}$ is added into a calorimeter containing $300 \mathrm{g}$ of cold water at $10°\mathrm{C}$, temperature of the mixture becomes $20°\mathrm{C}$. Then, a metallic block of mass $1 \mathrm{kg}$ at $10°\mathrm{C}$ is dipped into the mixture in the calorimeter. After reaching thermal equilibrium, the final temperature becomes $19°\mathrm{C}.$ What is the specific heat of the metal in CGS unit ?

A metallic block of mass $20 \mathrm{kg}$ is dragged with a uniform velocity of $0.5 {\mathrm{ms}}^{-1}$ on a horizontal table for $2.1 \mathrm{s}$. The coefficient of static friction between the block and the table is $0.10$. What will be the maximum possible rise in temperature of the metal block, if the specific heat of the block is $0.1 \mathrm{CGS}$ unit? Assume $g=10 {\mathrm{ms}}^{-2}$ and uniform rise in temperature throughout the whole block. [Ignore absorption of heat by the table]

Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the minimum speed required to make both the blocks melt completely, if the initial temperatures of the blocks were $-8°\mathrm{C}$ each? (Specific heat of ice is $2100 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$ and latent heat of fusion of ice is $3.36\times {10}^5 \mathrm{J} {\mathrm{kg}}^{-1})$

The water equivalent of a calorimeter is $10 \mathrm{g}$ and it contains $50 \mathrm{g}$ of water at $15°\mathrm{C}$. Some amount of ice, initially at $-10°\mathrm{C}$ is dropped in it and half of the ice melts till equilibrium is reached. What was the initial amount of ice that was dropped (when specific heat of ice $=0.5$cal ${\mathrm{gm}}^{-1}{}^{\circ }\mathrm{C}^{-1},$ specific heat of water $=1.0$cal ${\mathrm{gm}}^{-1\circ }{\mathrm{C}}^{-1}$ and latent heat of melting of ice $=80$ cal ${\mathrm{gm}}^{-1}$ )?