# Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of $T$.The total internal energy, U of a mole of this gas, and the value of $\gamma\left(=\frac{C_{p}}{C_{v}}\right)$ are given, respectively, by:

Question:

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of $T$.The total internal energy, U of a mole of this gas, and the value of $\gamma\left(=\frac{C_{p}}{C_{v}}\right)$ are given, respectively, by:

1. $U=\frac{5}{2}$ RT and $\gamma=\frac{6}{5}$

2. $\mathrm{U}=5 \mathrm{RT}$ and $\gamma=\frac{7}{5}$

3. $U=\frac{5}{2}$ RT and $\gamma=\frac{7}{5}$

4. $\mathrm{U}=5 \mathrm{RT}$ and $\gamma=\frac{6}{5}$

JEE Main Previous Year Single Correct Question of JEE Main from Physics Kinetic Teory chapter.

JEE Main Previous Year Sep. 06, 2020 (I)

Correct Option: 3

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 $=10 \mathrm{~ms}^{-2}$ ]

View Solution

error: Content is protected !!