Degree of Freedom

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

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

Q. $N$ moles of an ideal diatomic gas are in a closed cylinder at temperature $T$. Suppose, on supplying heat to the gas, its temperature remains constant, but $n$ moles get dissociated into atoms. Then, heat supplied to the gas is -

1. Zero
2. $\frac{1}{2}nRT$
3. $\frac{3}{2}nRT$
4. $\frac{3}{2}(N-n)RT$

Q. Two samples $\left(A\right)$ and $\left(B\right)$ of gas initially at the same temperature and pressure are compressed from a volume $\left(V\right)$ to a volume $\left(V/2\right)$. One isothermally and the other adiabatically respectively. The final pressure of

1. $A$ is less than that of $B$
2. $A$ is twice the pressure of $B$
3. $A$ is greater than that of $B$
4. $A$ is equal to that of $B$

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

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

Q. The molar specific heat capacity of an ideal gas, at constant pressure and at constant volume, are denoted by $C_p\text{and}{C}_v$, respectively. If $\gamma =\frac{C_p}{C_v}\text{and R}$ is the universal gas constant, then $C_v$ is equal to,

1. $\gamma R$
2. $\frac{1+\gamma }{1-\gamma }$
3. $\frac{R}{(\gamma -1)}$
4. $\frac{(\gamma -1)}{R}$

Q.

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:

1. $\frac{3}{2}RT$

2. $3RT$

3. $\frac{5}{2}RT$

4. $\frac{9}{2}RT$

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.

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. 

2. 

3. 

4. 

Q. A diatomic gas, with rigid molecules, does $10\text{J}$ of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process ?

1. $30\text{J}$
2. $40\text{J}$
3. $25\text{J}$
4. $35\text{J}$

Q. The amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from $273K$ to $373K$, when no work is done is ($R$ = universal gas constant)

1. $100R$
2. $150R$
3. $300R$
4. $500R$

Q. Two Perfect gases at absolute temperatures T1 and T2 are mixed. There is no loss of energy. Find the temperature of the mixture if the masses of the molecules are m1 and m2 and the number of molecules in the gases are $n_1$ and $n_2$.

1. 
2. 
3. 
4. 

Q. If 150 J of heat is added to a system and the work done by the system is 110 J, then change in internal energy will be

1. 260 J
2. 150 J
3. 110 J
4. 40 J

Q. An ideal diatomic gas undergoes a process AB, for which PV indicator diagram is shown. Temperature at state A is $T_0$. When process changes from endothermic to exothermic,
temperature of the gas is $\frac{175\alpha }{864}{T}_0$. Find the value of $\alpha$.

Q. The amount of heat needed to raise the temperature of $4$ moles of a rigid diatomic gas from $0^{\circ }\text{C}$ to ${50}^{\circ }\text{C}$, when no work is done, is -

$R$ is the universal gas constant.

1. $500R$
2. $750R$
3. $250R$
4. $175R$

Q. The amount of heat energy required to raise the temperature of $1\text{gm}$ of Helium at $\text{NTP}$, from $T_1\text{K}\text{to}{T}_2\text{K}$ is-

1. $\frac{3}{4}N{k}_B\left(\frac{T_2}{T_1}\right)$
2. $\frac{3}{8}N{k}_B(T_2-T_1)$
3. $\frac{3}{2}N{k}_B(T_2-T_1)$
4. $\frac{3}{4}N{k}_B(T_2-T_1)$

Q.

A cylinder rolls without slipping down an inclined plane, the number of degrees of freedom it has, is

1. 2

2. 3

3. 5

4. 1

Q. 13.An object O is just about to strike a perfectly reflecting inclined plane of inclination 37 degree. Its velocity is 5 m/s. Find the velocity of its image (i)3i + 4j (ii)4i + 3j (iii)4.8i + 1.4j (iv) 1.4i + 4.8j

Q. A diver under water looks obliquely at a fisherman s†an ding on the bank of lake ? Will the fisherman appear taller or shorter to diver ? G

Q. Starting at temperature $300\text{K}$, one mole of an ideal diatomic gas $(\gamma =1.4)$ is first compressed adiabatically from volume $V_1$ to $V_2=\frac{V_1}{16}$. It is then allowed to expand isobarically to volume $2V_2$. If all the processes are the quasi-static, then the final temperature of the gas (in $K$) is (to the nearest integer)

Q. One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume vs. temperature (V-T) diagram. The correct statement(s) is/are [$R$ is the gas constant]

1. The above thermodynamic cycle exhibits only isochoric and adiabatic processes
2. The ratio of heat transfer during processes $1\to 2$ and $3\to 4$ is $\left|\frac{Q_{1-2}}{Q_3-4}\right|=\frac{1}{2}$
3. The ratio of heat transfer during processes $1\to 2$ and $2\to 3$ is $\left|\frac{Q_{1-2}}{Q_{2-3}}\right|=\frac{5}{3}$
4. Work done in this themodynamic cycle $(1\to 2\to 3\to 4\to 1)$ is $|W|=\frac{1}{2}R{T}_0$

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. 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. If $\gamma$ be the ratio of molar heat capacity of an ideal gas, then degree of freedom for the molecule of gas is

1. $\frac{25}{2}(\gamma -1)$
2. $\frac{3\gamma -1}{2\gamma -1}$
3. $\frac{2}{\gamma -1}$
4. $\frac{\gamma }{2}(\gamma -1)$

Q.

The absolute temperature of air in a region linearly increases from $T_1$ to $T_2$ in a space of width $d$. Find the time taken by a sound wave to go through the region in terms of$T_1$, $T_2$, $d$ and the speed $V$ of sound at $273K$. Evaluate this time for $T_1=280K,T_2=310K,d=33m\text{and}V=330m{s}^{-1}$.

Q.

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by $P{V}^n$ = constant, then n is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively):

1. 

2. 

3. 

4. 

Q. In the above question, if $\gamma =1.5$ the gas may

1. a mixture of monoatomic and diatomic gas
2. a mixture of diatomic and triatomic gas
3. diatomic
4. monoatomic

Q. The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is?

1. $6.25\%$
2. $26.8\%$
3. $12.5\%$
4. $20\%$

Q. One mole of oxygen gas having a volume equal to 22.4 litres at $0^{\circ }C$ and 1 atm pressure is compressed isothermally so that it's volume reduces to 11.2 litres. What is the work done in this process?

Q. Find the change in the internal energy of the system in each of situation in Column I.
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i. A system absorbs}500\text{cal of heat and}& a.-5000J\\ \text{at the same time does}400J\text{of work}& \\ \text{ii. A system absorbs}300\text{cal and at the}& b.1692J\\ \text{same time}420J\text{of work is done on it}& \\ \text{iii. Twelve hundred calories heat is removed}& c.1680J\\ \text{from a gas held at constant volume}& \end{array}$

1. i-b, ii-c, iii-a
2. i-c, ii-b, iii-a
3. i-b, ii-a, iii-a
4. i-b, ii-a, iii-c

Q. The ratio of the specific heats $\frac{C_p}{C_v}=\gamma$ in terms of degree of freedom (n) is given by:

1. $(1+\frac{2}{n})$
2. $(1+\frac{n}{2})$
3. $(1+\frac{n}{3})$
4. $(1+\frac{1}{n})$