B M Sharma Solutions for Chapter: Thermometry, Thermal Expansion and Calorimetry, Exercise 3: Exercises

A cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap as shown. On heating the system
 

If a graph is plotted taking the temperature in Fahrenheit along the Y-axis, and the corresponding temperature in Celsius along the X-axis, then the graph will be a straight line,

The temperature of an isotropic cubical solid of length $l_0$, density ${\rho }_0$ and coefficient of linear expansion $\alpha$ is increased by $20°\mathrm{C}$. Then at higher temperature, to a good approximation:-

$2 \mathrm{kg}$ of ice at $-15°\mathrm{C}$ is mixed with $2.5 \mathrm{kg}$ of water at $25°\mathrm{C}$ in an insulating container. If the specific heat capacities of ice and water are $0.5 \mathrm{cal}/\mathrm{g}°\mathrm{C}$ and $1 \mathrm{cal}/\mathrm{g}°\mathrm{C}$, find the amount of water present in the container? (in $\mathrm{kg}$ nearest integer)

A clock with a metallic pendulum at $15°\mathrm{C}$ runs faster by $5 \mathrm{s}$ each day and at $30°\mathrm{C}$, runs slow by $10 \mathrm{s}$. Find the coefficient of linear expansion of the metal. (nearly in ${10}^{-5}/{}^{\circ }\mathrm{C}$)

Two vessels connected at the bottom by a thin pipe with a sliding plug contain liquid at $20°\mathrm{C}$ and $80°\mathrm{C}$ respectively. The coefficient of cubic expansion of liquid is ${10}^{-3}{ \mathrm{K}}^{-1}$. The ratio of heights of liquid columns in the vessel $\left(h_{20}/h_{80}\right)$ is nearest to which integer?

Three rods of equal length $l$ are joined to form an equilateral triangle $PQR$. $O$ is the mid point of $PQ$. Distance $OR$ remains the same for small change in temperature. Coefficient of linear expansion $PR$ and $RQ$ is the same, i.e., ${\alpha }_2$ but that for $PQ$ is ${\alpha }_1$. Then find the ratio ${\alpha }_1:{\alpha }_2$.

A block of ice of mass $M=13.44 \mathrm{kg}$ slides on a horizontal surface. It starts with a speed of $v=10 \mathrm{m}/\mathrm{s}$ and finally stops after moving a distance of $s=30 \mathrm{m}$. What is the mass of ice (in grams) that has melted due to friction between the block and the surface? Latent heat of fusion of ice is $L_{\mathrm{f}}=80 \mathrm{cal}/\mathrm{g}$