One kg of a diatomic gas is at a pressure of $8 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$. The density of the gas is $4 \mathrm{~kg} / \mathrm{m}^{3}$. What is the energy of the gas due to its thermal motion?

Question:

One kg of a diatomic gas is at a pressure of $8 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$. The density of the gas is $4 \mathrm{~kg} / \mathrm{m}^{3}$. What is the energy of the gas due to its thermal motion?

1. $5 \times 10^{4} \mathrm{~J} 2.$6 \times 10^{4} \mathrm{~J}$3.$7 \times 10^{4} \mathrm{~J}$4.$3 \times 10^{4} \mathrm{~J}$JEE Main Previous Year Single Correct Question of JEE Main from Physics Kinetic Teory chapter. JEE Main Previous Year 2009 Correct Option: 1 Solution: Related Questions • The number density of molecules of a gas depends on their distance$r$from the origin as,$n(r)=n_{0} e^{-\alpha r 4}$. Then the total number of molecules is proportional to: View Solution • A vertical closed cylinder is separated into two parts by a frictionless piston of mass$m$and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is$l_{1}$, and that below the piston is$l_{2}$, such that$l_{1}>l_{2}$. Each part of the cylinder contains$\mathrm{n}$moles of an ideal gas at equal temperature T. If the piston is stationary, its mass,$m$, will be given by:$(\mathrm{R}$is universal gas constant and$\mathrm{g}$is the acceleration due to gravity) View Solution • The temperature of an open room of volume$30 \mathrm{~m}^{3}$increases from$17^{\circ} \mathrm{C}$to$27^{\circ} \mathrm{C}$due to sunshine. The atmospheric pressure in the room remains$1 \times 10^{5} \mathrm{~Pa}$. If$n_{i}$and$n_{f}$are the number of molecules in the room before and after heating, then$n_{f}-n_{i}$will be : View Solution • For the P-V diagram given for an ideal gas, out of the following which one correctly represents the T-P diagram? View Solution • There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment 1 is filled with an ideal gas and Compartment 3 is filled with a real gas. Compartments 2 and 4 are vacuum. A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum. Statement-1: No change in the temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands in vacuum. Statement-2: The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential. View Solution • Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will View Solution • Number of molecules in a volume of$4 \mathrm{~cm}^{3}$of a perfect monoatomic gas at some temperature$T$and at a pressure of$2 \mathrm{~cm}$of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is$4 \times 10^{-14} \mathrm{erg}, g=980 \mathrm{~cm} / \mathrm{s}^{2}$, density of mercury$=13.6 \mathrm{~g} / \mathrm{cm}^{3}$) View Solution • For a given gas at$1 \mathrm{~atm}$pressure, rms speed of the molecules is$200 \mathrm{~m} / \mathrm{s}$at$127^{\circ} \mathrm{C}$. At$2 \mathrm{~atm}$pressure and at$227^{\circ} \mathrm{C}$, the rms speed of the molecules will be: View Solution • If$10^{22}$gas molecules each of mass$10^{-26} \mathrm{~kg}$collide with a surface (perpendicular to it) elastically per second over an area$1 \mathrm{~m}^{2}$with a speed$10^{4} \mathrm{~m} / \mathrm{s}$, the pressure exerted by the gas molecules will be of the order of: View Solution • The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to: [Boltzmann Constant$k_{\mathrm{B}}=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$Avogadro Number$\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{26} / \mathrm{kg}$Radius of Earth :$6.4 \times 10^{6} \mathrm{~m}$Gravitational acceleration on Earth$=10 \mathrm{~ms}^{-2}\$ ]

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