Degree of Freedom

Q.

At room temperature, the number of degrees of freedom of linear diatomic molecule is

1. 3

2. 4

3. 5

4. 6

Q. Molar heat capacity at constant pressure for a non-linear triatomic gas is

1. $\frac{3R}{2}$
2. $\frac{5R}{2}$
3. $4R$
4. $2R$

Q.

If the degree of freedom of a gas are f, then the ratio of two specific heats $\frac{C_p}{C_v}$ is given by

1. $\frac{2}{f}+1$

2. $1-\frac{2}{f}$

3. $1+\frac{1}{f}$

4. $1-\frac{1}{f}$

Q. If the degrees of freedom of a gas molecule be f, then the ratio of two specific heat capacities $\frac{C_P}{C_V}$ is given by

1. $\frac{2}{f}+1$
2. $1-\frac{2}{f}$
3. $1+\frac{1}{f}$
4. $1-\frac{1}{f}$

Q. For a gas $\frac{R}{C_V}=0.4$. The gas is made up of molecules which are

1. Diatomic
2. Mixture of diatomic and polyatomic molecules
3. Monoatomic
4. Polyotomic

Q.

At room temperature, the number of degrees of freedom of linear diatomic molecule is

1. 3

2. 4

3. 5

4. 6

Q.

We know that, for an ideal monoatomic gas, the total internal energy is a result of the translational kinetic energy only. For the oxygen molecule $O_2$ (assume it doesn't oscillate along the bond axis), which rotates as well as translates, choose the correct statement(s) from the following

1. Change in translational kinetic energy of a sample of n moles = $n{C}_V\Delta T$

2. Translational kinetic energy < rotational kinetic energy

3. Translational kinetic energy > rotational kinetic energy
4. Translational kinetic energy = rotational kinetic energy.

Q.

We know that, for an ideal monoatomic gas, the total internal energy is a result of the translational kinetic energy only. For the oxygen molecule $O_2$ (assume it doesn't oscillate along the bond axis), which rotates as well as translates, choose the correct statement(s) from the following

1. Change in translational kinetic energy of a sample of n moles = $n{C}_V\Delta T$

2. Translational kinetic energy < rotational kinetic energy

3. Translational kinetic energy > rotational kinetic energy
4. Translational kinetic energy = rotational kinetic energy.

Q. A container made up of insulating material contains 4 moles of an ideal diatomic gas at temperature $T$. Heat $Q$ is supplied to this gas, due to which 2 moles of the gas are dissociated into atoms, but the temperature of the gas remains constant. Find the option that correctly represents the relation between $Q$ and $T$.

1. $Q=2RT$
2. $Q=RT$
3. $Q=3RT$
4. $Q=4RT$

Q.

Two perfect gases at absolute temperatures $T_{1}and{T}_2$ are mixed. There is no loss of energy in this process. If $n_{1}and{n}_2$ are the respective number of molecules of the gases, the temperature of the mixture will be

1. $\frac{n_1{T}_1+n_2{T}_2}{n_1+n_2}$
   

2. $\frac{n_2{T}_1+n_1{T}_2}{n_1+n_2}$
   

3. $T_1+\frac{n_2}{n_1}{T}_2$
   

4. $T_2+\frac{n_1}{n_2}{T}_1$

Q. The ratio of average translational kinetic energy to rotational kinetic energy of a diatomic molecule at temperature T is

1. $3$
2. $\frac{7}{5}$
3. $\frac{5}{3}$
4. $\frac{3}{2}$

Q. If the distance between the atoms of a diatomic gas remains constant. Its specific heat capacity at constant volume per gram-mole is

1. $\frac{5}{2}R$
2. $\frac{2}{3}R$
3. $R$
4. $\frac{R}{3}$

Q. Which of the following options are correct regarding the molar heat capacity $\left(C\right)$ for the gas whose $PV$ graph is shown below.

1. $C=\infty$
2. $C=0$
3. $C=R$
4. $C=2R$

Q. Which of the following options are correct regarding the molar heat capacity $\left(C\right)$ for the gas whose $PV$ graph is shown below.

1. $C=\infty$
2. $C=0$
3. $C=R$
4. $C=2R$

Q. An ideal gas having initial pressure $P$ volume $V$ and temperature $T$ is allowed to expand adiabatically until its volume becomes $5.66V$, while its temperature falls to $T/2$. Find the number of degrees of freedom of the gas molecule.
(Take $(5.66{)}^{0.4}=2)$

1. $2$
2. $3$
3. $5$
4. $6$

Q. For a gas $\frac{R}{C_V}=0.4$. The gas is made up of molecules which are

1. Diatomic
2. Mixture of diatomic and polyatomic molecules
3. Monoatomic
4. Polyotomic