Chittaranjan Dasgupta and Asok Kumar Das Solutions for Chapter: Thermal Expansion, Exercise 1: EXERCISE

A scale made of steel, is correct at $15°C$. A certain distance measured with this scale at $30°C$, is found to be $600 \mathrm{m}$. Find the error in measurement ($\alpha$ for steel$=0.000011$ per $°C$).

An ideal gas is initially at temperature $T$ and volume $V$. Its volume is increased by $∆V$ due to increase in temperature $∆T$, pressure remaining constant. The quantity $\delta =\frac{\mathrm{\Delta V}}{\mathrm{V}\cdot \mathrm{\Delta T}}$ varies with temperature as

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of the gas in $A$ is $m_A$ and that in $B$ is $m_B$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2V$. The change in the pressure in $A$ and $B$ are found to be $∆p$ and $1.5 ∆p$ respectively. Then

The densities of a liquid at $0°\mathrm{C}$ and $100°\mathrm{C}$ are respectively $1.0127$ and $1$. A specific gravity bottle is filled with $300 \mathrm{g}$ of the liquid at $0°\mathrm{C}$ upto the brim and it is heated to $100°\mathrm{C}$. Then the mass of the liquid expelled in grams is (coefficient of linear expansion of glass$=9\times 10-6^{\circ }\mathrm{C}-1$)

The pressure that has to be applied to the ends of a steel wire of length $10 \mathrm{cm}$ to keep its length constant when its temperature is raised by $100°\mathrm{C}$ is: (For steel Young’s modulus is $2\times 1011 {\mathrm{Nm}}^{-2}$ and coefficient of thermal expansion is $1.1\times {10}^{-5} {\mathrm{K}}^{-1}$)

A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L$, $\alpha$ and $Y$ respectively denote the length of the rod, coefficient of linear thermal expansion and Young’s modulus of its material, then for an increase in temperature of the rod by $∆T$, the longitudinal stress developed in the rod is

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $2:3$. The ratio of their partial pressures, when inclosed in a vessel kept at a constant temperature, is $4:3$. The ratio of their densities is

Draw $p-\frac{1}{V}$ graphs for a given mass of a gas at three constant temperatures $T_1$, $T_2$ and $T_3$ $\left(T_1<T_2<T_3\right)$.