B M Sharma Solutions for Chapter: Kinetic Theory Of Gases, Exercise 2: DPP

The initial temperature of a gas is $100 °\mathrm{C}$. The gas is contained in a closed vessel. If the pressure of the gas is increased by $5\%$. Calculate the increase in temperature of the gas.

A closed hollow insulated cylinder is filled with gas at $0 °\mathrm{C}$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to $100 °\mathrm{C}$. If the piston moves $5 \mathrm{cm}$, the length of the hollow cylinder is

The airtight and smooth pistons of a cylindrical vessel are connected with a string, as shown, initially, pressure and temperature of the gas are $P_0$ and $T_0$. The atmospheric pressure is also $P_0$. At a later time, the tension in the string is $\frac{3}{8}{P}_{0}A$ where $A$ is the cross-sectional area of the cylinder. At this time, the temperature of the gas has become

$P‐T$ graph for the same number of moles of two ideal gases is shown in the figure. Find the path along which volume decreases.

A vessel of volume $V=30 \mathrm{litre}$ is separated into three equal parts by stationary semipermeable membranes. The left, middle and right parts are filled with $m_{\mathrm{H}}=30 \mathrm{g}$ of hydrogen, $m_{O_2}=160 \mathrm{g}$ of oxygen and $m_{\mathrm{N}}=70 \mathrm{g}$ of nitrogen respectively. The left partition lets through the only hydrogen while the right partition lets through hydrogen and nitrogen. If the temperature in all is $300 \mathrm{K}$, the ratio of pressure in the three compartments will be?

A steel tank contains $300 \mathrm{g}$ of ammonia gas $\left({\mathrm{NH}}_3\right)$ at a pressure of $1.35\times {10}^6 \mathrm{Pa}$ and a temperature of $77 °\mathrm{C}$. Later the temperature is $22 °\mathrm{C}$ and the pressure is $8.7\times {10}^5 \mathrm{Pa}$.

Which of the following quantities is independent of the nature of the gas at same temperature?

Which of the following quantities depend on temperature only for a given ideal gas?