The volume thermal expansion coefficient of an ideal gas at constant pressure is

An air bubble starts rising from the bottom of a lake. Its diameter is $3.6 \mathrm{mm}$ at the bottom and $4 \mathrm{mm}$ at the surface. The depth of the lake is $2.5 \mathrm{m}$ and the temperature at the surface is $40°\mathrm{C}$. What is the temperature at the bottom of the lake? Assume that the variation of density of water with depth is negligible. Atmospheric pressure is $76 \mathrm{cm}$ of $Hg$ and $g=980 {\mathrm{cm} \mathrm{s}}^{-2}$.

The volume of a certain mass of gas at constant pressure increases from $1$ litre to $1.128$ litre due to an increase of temperature from $0°\mathrm{C}$ to $35°\mathrm{C}$. From these data, find the value of absolute zero.

The volume occupied by a certain mass of gas at $27°\mathrm{C}$ and $740 \mathrm{mm}$ of mercury pressure is $400 {\mathrm{cm}}^3$. If the temperature be changed to $0°\mathrm{C}$ and pressure to $760 \mathrm{mm}$ of mercury, what would be the volume of the gas?

An air bubble gradually rises from a depth of $10 \mathrm{m}$ in a lake where the temperature is $10°\mathrm{C}$ to the surface where the temperature is $25°\mathrm{C}$. Compare the radii of the bubble in the two places. Atmospheric pressure $=75 \mathrm{cm}$ of $Hg$ and density of mercury $=13.6 \mathrm{g} {\mathrm{cm}}^{-3}$.

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

A gas expands in such a manner that its pressure and volume comply the condition $p{V}^2=$ constant. Find out whether the gas is heated or cooled during such an expansion.

The measurement of a room is $15 \mathrm{m}\times 12 \mathrm{m}\times 8 \mathrm{m}$. If the temperature of the room increases from $22°\mathrm{C}$ in the morning to $30°\mathrm{C}$ at noon, calculate what percentage of the air will be expelled from the room, pressure remaining constant.

A glass vessel contains air at $42°\mathrm{C}$. To what temperature must it be heated to expel $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$th of the air, pressure remaining constant?

The volume of a gas is doubled by changing its temperature at constant pressure. The initial temperature of the gas was $13°\mathrm{C}$. Calculate the final temperature.

A vessel of volume $V=0.03 {\mathrm{m}}^3$ contains an ideal gas at $0°\mathrm{C}$. After a portion has escaped from the vessel, the pressure decreases by $P=0.78$ atmosphere (temperature remaining constant). Find the mass of the gas escaped. The density under normal conditions ${\rho }_0=1.3 \mathrm{kg} {\mathrm{m}}^{-3}$.

A capillary glass tube with fine bore has both the ends sealed and a small mercury pellet inside. The pellet divides the tube into two parts whose lengths are in the ratio of $3:1$. If the initial temperature of the whole arrangement is $0°\mathrm{C}$ and if it is heated afterwards to $273°\mathrm{C}$ what will be the change in the air pressure inside the tube?

A bulb $A$ of volume $V_1$ is connected to another bulb $B$ of volume $V_2$ by a narrow tube of negligible volume. The two bulbs were initially at the same temperature $T_1$ and pressure $p_1$. Now $A$ is heated to a temperature $T_2$. Find the new pressure $P_2$ and show the fraction of the original mass of air that stays in the bulb $A$ is.