Degrees of Freedom & Internal Energy

The internal energy of a diatomic molecule (air) in $4\text{ m} \times 4\text{ m} \times 3\text{ m}$ sized room at $10^{5}$ N/m$^{2}$ atmospheric pressure will be $x \times 10^{6}$ J. The value of $x$ is

If 2 mole of an ideal monoatomic gas at temperature $T$, is mixed with 6 mole of another ideal monoatomic gas at temperature $2T$ then the temperature of mixture is:

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is ______.

A rigid diatomic gas having molar mass m is contained in an insulated container. The container is moving with velocity V. If it is stopped suddenly, the change in temperature is (R - gas constant)

An insulated container contains a monoatomic gas of molar mass 'm'. The container is moving with velocity 'V'. If it is stopped suddenly, the change in temperature of the gas is (R-gas constant)

Match the List I with List II

Choose the correct answer from the options given below:

500 gram of a diatomic gas is enclosed at a pressure of $10^{5}\text{ N m}^{-2}$. The density of the gas is $5\text{ kg m}^{-3}$. The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator]

The internal energy of air in $4\text{ m} \times 4\text{ m} \times 3\text{ m}$ sized room at 1 atmospheric pressure will be___________________ $\times 10^{6}\text{ J}$

(Consider air as diatomic molecule)

The translational degrees of freedom $(f_t)$ and rotational degrees of freedom $(f_r)$ of $\text{CH}_4$ molecule are:

Energy of 10 non rigid diatomic molecules at temperature $T$ is:

A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

$N$ moles of a polyatomic gas $(f = 6)$ must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of $N$ is:

An insulated container contains a diatomic gas of molar mass ' m '. The container is moving with velocity ' $V$ ', if it is stopped suddenly, the change in temperature is ( $R =$ gas constant)

An insulated container contains a monoatomic gas of molar mass ' $m$ '. The container is moving with velocity ' $V$ '. If it is stopped suddenly, the change in temperature is ( $R =$ gas constant)

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed $(v_{\text{rms}})$ and choose the correct answer from the options given below:

Match List I with List II:

Choose the correct answer from the options given below:

The internal energy of a monoatomic ideal gas molecule is

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

An insulated container contains a monoatomic gas of molar mass '$m$'. The container is moving with velocity '$V$'. If it is stopped suddenly, the change in temperature of a gas is [R is gas constant]

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following is:

The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _____________ J. (Given R = 8.31 J/mol.K)

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel, temperature of the gas increases by:

(R = universal gas constant)

Internal energy of $n_1$ moles of hydrogen at temperature '$T$' is equal to internal energy of '$n_2$' moles of helium at temperature $2T$, then the ratio $n_1 : n_2$ is

[Degree of freedom of $\text{He} = 3$, Degree of freedom of $\text{H}_2 = 5$]

Two ideal polyatomic gases at temperatures T1 and T2 are mixed so that there is no loss of energy. If F1 and F2, m1 and m2, n1 and n2 be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is:

The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is:

The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U $=$ 3PV + 4. The gas is:

A monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R = gas constant) is $\frac{x}{3R}$. Value of x is ___________.

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:

Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is:

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is:

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to _______.

Initially a gas of diatomic molecules is contained in a cylinder of volume V1 at a pressure P1 and temperature 250 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 K, when contained in a volume 2V1 is given by P2. The ratio $\frac{P_2}{P_1}$ is ________.

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. considering only translational and rotational modes, the total internal energy of the system is:

Two kg of a monoatomic gas is at a pressure of 4 $\times$ 104 N/m2. The density of the gas is 8 kg/m3. What is the order of energy of the gas due to its thermal motion?

A gas mixture consists of 2 moles of O2 and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is

N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas?

This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements.

Statement 1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.

Statement 2: A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.

Three perfect gases at absolute temperatures $T_1, T_2$ and $T_3$ are mixed. The masses of molecules are $m_1, m_2$ and $m_3$ and the number of molecules are $n_1, n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is:

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma.$ It is moving with speed $v$ and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:

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

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0,$ while Box contains one mole of helium at temperature $\left(\frac{7}{3}\right)T_0.$ The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, $T_f$ in terms of $T_0$ is

To find out degree of freedom, the expansion is

The degrees of freedom of a molecule of a triatomic gas are

The number of translational degrees of freedom for a diatomic gas is

Three containers of the same volume contain three different gases. The masses of the molecules are $m_1, m_2$ and $m_3$ and the number of molecules in their respective containers are $N_1, N_2$ and $N_3$. The gas pressure in the containers are $P_1, P_2$ and $P_3$ respectively. All the gases are now mixed and put in one of these containers. The pressure $P$ of the mixture will be