Embibe Experts Solutions for Chapter: Kinetic Theory of Gases, Exercise 1: Exercise 1

$V$-$T$ diagram for a process of a given mass of ideal gas is as shown in the figure. During the process, the pressure of the gas

One mole of an ideal gas is kept enclosed under a light piston (area $={10}^{-2} {\mathrm{m}}^2$) connected by a compressed spring (spring constant $100 \mathrm{N} {\mathrm{m}}^{-1}$). The volume of gas is $0.83 {\mathrm{m}}^3$ and its temperature is $100 \mathrm{K}$. The gas is heated so that it compresses the spring further by $0.1 \mathrm{m}$. The work done by the gas in the process is (Take $R=8.3 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mole}}^{-1}$ and suppose there is no atmosphere).

An ideal gas undergoes a thermodynamic cycle as shown in figure.

Which of the following graphs may represent the same cycle?

The ratio of r.m.s. speed to the r.ms. angular speed of a diatomic gas at a certain temperature is: (assume $m=$ mass of one molecule, $M=$ molecular mass, $I=$ moment of inertia of the molecules)

Which of the following will have maximum total kinetic energy at temperature $300 \mathrm{K}$.

Initially a gas of diatomic molecules is contained in a cylinder of volume $V_1$ at a pressure $P_1$ and temperature $250 \mathrm{K}.$ Assuming that $25\%$ of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature $2000 \mathrm{K},$ when contained in a volume $2 {\mathrm{V}}_1$is given by $P_2.$ The ratio $\frac{P_2}{P_1}$ is_____.

A container is divided into two chambers by a partition. The volume of first chamber is $4.5$ litre and second chamber is $5.5$ litre. The first chamber contain $3.0$ moles of gas at pressure $2.0$ atm and second chamber contain $4.0$ moles of gas at pressure $3.0$ atm. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is $x\times {10}^{-1}$ atm. Value of $x$ is

At low temperatures, the molar heat capacity of solids at constant pressure depends on the absolute temperature $T$ according to the law $C_T=C_{T_0}{\left(\frac{T}{T_0}\right)}^3.$ One mole $(40 \mathrm{g})$ of solid argon at temperature $8 \mathrm{K}$ is brought into thermal contact with $2 \mathrm{kg}$ of solid argon at a temperature of $1 \mathrm{K}$ and they insulated everything together. What will be the temperature (in $\mathrm{K}$ ) of the substance when thermal equilibrium is established? Round off to nearest integer.