Kinetic theory of gases practice · Mixed difficulty

The relation between the gas pressure $P$ and average kinetic energy per unit volume $E$ is

Relation between the ratio of specific heats $\left( \gamma \right)$ of gas and degree of freedom 'f' will be

Consider a gas with density $\rho$ and ${\bar c}$ as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity $v,\;$ then the pressure exerted by the gas is

A monoatomic gas is kept at room temperature 300K. Calculate the average kinetic energy of gas molecule (Use $k = 1.38 \times {10^{ - 23}}MKS$ units)

Read the given statements and decide which is/are correct on the basis of kinetic theory of gases
(I) Energy of one molecule at absolute temperature is zero
(II) $r.m.s.$speeds of different gases are same at same temperature
(III) For one gram of all ideal gas kinetic energy is same at same temperature
(IV) For one mole of all ideal gases mean kinetic energy is same at same temperature

Given below are two statements :

Statement I : The temperature of a gas is $-73^{\circ} \mathrm{C}$. When the gas is heated to $527^{\circ} \mathrm{C}$, the root mean square speed of the molecules is doubled.

Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.

In the light of the above statements, choose the correct answer from the options given below:

Assertion: A gas has a unique value of specific heat.
Reason: Specific heat is defined as the amount of heat required to raise the temperature of unit mass of the substance through unit degree.

A monoatomic gas molecule has

A gas consisting of rigid diatomic molecules is expanded adiabatically. How many time has the gas to be expanded to reduce the root mean square velocity of the molecules $\eta=1.50$ times.

Water is used to cool radiators of engines, because

Molecules of a gas behave like

The root mean square velocity of the molecules of a gas is $1260 \mathrm{~m} / \mathrm{s}$. The most probable speed of the molecules is

The Molecules of a given mass of a gas have r.m.s. Velocity of $200ms_{}^{ - 1}\,at\,{27^0}C$ and $1.0 \times {10^5}N{m^{ - 2}}$ pressure. When the temperature and pressure of the gas are respectively, ${127^0}C{\mkern 1mu} {\mkern 1mu} and{\mkern 1mu} {\mkern 1mu} 0.05 \times {10^5}N{m^{ - 2}}$ , The r.m.s velocity of its molecule in $\;ms_{}^{ - 1}$ is

The speeds of 5 molecules of a gas (in arbitary units) are as follows : 2,3,4,5,6. The r.m.s speed for these molecules is

Assertion: Mean free path of a gas molecules varies inversely as density of the gas.
Reason: Mean free path varies inversely as pressure of the gas.

For a gas molecule with a 6 degrees of freedom the law of equipartition of energy gives the following relation between the molar specific heat $\left( {Cv} \right)$ and gas constant $\left( R \right)$

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1: 4$, then
A. The r.m.s. velocity of gas molecules in two vessels will be the same.
B. The ratio of pressure in these vessels will be $1 : 4$.
C. The ratio of pressure will be $1 : 1$.
D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $1 : 4$.
Choose the correct answer from the options given
below

The translational kinetic energy of gas molecule for one mole of the gas is equal to

Assertion (A) : If a gas container is placed in a moving train, the temperature of gas will increase.

Reason (R) : Kinetic energy of gas molecules will increase.

One mole of an ideal gas undergoes a process: $P=\frac{P_o}{1+\left(V_o / V\right)^2}$. Here $P_o$ and $V_o$ are constants. Change in temperature of the gas when volume is changed from $V=V_o$ to $V=2 V_o$ is

Assertion: An ideal gas has infinitely many molar specific heats.
Reason: Specific heat is amount of heat needed to raise the temperature of 1 mole of gas by $1 \mathrm{~K}$.

Let $\mathrm{V}$ denote the root mean square speed of the molecules in an ideal diatomic gas at absolute temperature $\mathrm{T}$. The mass of a molecule is ' $m$ '. Neglecting vibrational energy terms, which is false?

A sample of gas is ${0^0}C$. To what temperature it must be raised in order to double the r.m.s. speed
of the molecule

The specific heats, ${C_p}\mathrm{ \,\,and }\,\,{C_V}$ of a gas of diatomic molecules, A are given (in units of $\mathrm{J mo}{\mathrm{l}^{ - 1}}{K^{ - 1}}$) by 29 and 22, respectively. Another gas of diatomic molecules B, has the corresponding values 30 and 21. If they are treated as ideal gases, then

The temperature at which the ‘rms’ speed of an atom. In an argon gas cylinder is equal to the ‘rms’ speed of a helium gas atom at $- 20^\circ \,C$ is (Atomic mass) of argon and that of helium = 4.04)

If the rms velocity of a gas is $v$ ,then

An electron tube was sealed off during manufacture at a pressure of $1.2 \times {10^{ - 7}}mm$ of mercury of $27^\circ C.$ If volume is $1000\,c{m^3},$. The number of molecules that remains in the tube is

The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K, the root mean square velocity of the gas molecule is V. at 480 K it becomes

Assertion: Vibrational degree of freedom of a di-atomic gas molecule appears at very high temperature
Reason: Di-atomic gas has two vibrational degree of freedom in one direction.

$0.014 \mathrm{~kg}$ of nitrogen is enclosed in a vessel at a temperature of $27^{\circ} \mathrm{C}$. How much heat has to be transferred to the gas to double the r.m.s. velocity of its molecules?