Embibe Experts Solutions for Chapter: Thermal Properties of Matter, Exercise 3: Exercise-3

Liquid oxygen at $50 \mathrm{K}$ is heated to $300 \mathrm{K}$ at constant pressure of $1 \mathrm{atm}$. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?

An aluminium sphere of $20 \mathrm{cm}$ diameter is heated from $0 °\mathrm{C}$ to $100 °\mathrm{C}$. Its volume changes by (given that coefficient of linear expansion for aluminium ${\alpha }_{{\mathrm{A}}_1}=23\times {10}^{-6} °{\mathrm{C}}^{-1}$)

A pendulum clock lose $12 \mathrm{s}$ a day if the temperature is, $40°\mathrm{C}$ and gains, $4 \mathrm{s}$ a day if the temperature is, $20°\mathrm{C}.$ The temperature at which the clock will show correct time, and the co-efficient of linear expansion $\left(\alpha \right)$ of the metal of the pendulum shaft are respectively :

A copper ball of mass $100 \mathrm{gm}$ is at a temperature $T$. It is dropped in a copper calorimeter of mass $100 \mathrm{gm}$, filled with $170 \mathrm{gm}$ of water at room temperature. Subsequently, the temperature of the system is found to be $75 °\mathrm{C}$. $T$ is given by: (Given: room temperature $=30 °\mathrm{C}$, the specific heat of copper $=0.1 \mathrm{cal} {\mathrm{gm}}^{-1}°{\mathrm{C}}^{-1}$)

An unknown metal of mass $192 \mathrm{g}$ heated to a temperature of $100 °\mathrm{C}$ was immersed into a brass calorimeter of mass $128 \mathrm{g}$ containing $240 \mathrm{g}$ of water at a temperature of $8.4°\mathrm{C}$. Calculate the specific heat of the unknown metal, if water temperature stabilises at $21.5 °\mathrm{C}$. (Take, the specific heat of brass is $394 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$)

A metal ball of mass $0.1 \mathrm{kg}$ is heated upto $500 °\mathrm{C}$ and dropped into a vessel of heat capacity $800 \mathrm{J} {\mathrm{K}}^{-1}$ and containing $0.5 \mathrm{kg}$ water. The initial temperature of water and vessel is $30 °\mathrm{C}$. What is the approximate percentage increment in the temperature of the water? [Take specific heat capacities of water and metal are, respectively, $4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$ and $400 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$]

If $C_{\mathrm{p}}$ and $C_{\mathrm{v}}$ denote the specific heats (per unit mass) of an ideal gas of molecular weight $M\mathit{,}$ where $R$ is gas constant, then

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at $100°\mathrm{C}$, while the other one is at $0°\mathrm{C}$. If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is