Equipartition Theorem

Q. If 2 moles of an ideal monoatomic gas at temperature $T_0$ is mixed with 4 moles of another ideal monoatomic gas at temperature $2T_0$ in a closed vessel, then the temperature of the mixture is

1. $\frac{5}{3}{T}_0$
2. $\frac{3}{2}{T}_0$
3. $\frac{4}{3}{T}_0$
4. $\frac{5}{4}{T}_0$

Q. A mixture of ideal gases has 2 moles of Helium, 4 moles of Oxygen and 1 mole of Ozone at absolute temperature $T$. The internal energy of mixture is

1. $13\text{RT}$
2. $11\text{RT}$
3. $16\text{RT}$
4. $14\text{RT}$

Q. A proton, when accelerated through a potential difference of $V\text{volts}$ has a wavelength $\lambda$ associated with it. If an $\alpha -$ particle is to have the same wavelength $\lambda ,$ it must be accelerated through a potential difference of $V/n\text{volts}.$ The value of $n$ is

Q. The energy of a gas/litre is 300 joules, then its pressure will be

1. 
2. 
3. 
4. 

Q. If the ratio of specific heat of a gas at constant pressure to that at constant volume is $\gamma$, the change in internal energy of a mass of gas, when the volume changes from $V$ to $2V$ at constant pressure $P$, is :-

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

Q. If the door of a refrigerator is kept open, then which of the following is true?

1. Room is cooled
2. Room is heated
3. Room is either cooled or heated
4. Room is neither cooled nor heated

Q.

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

Q.
A container AB in the shape of a rectangular parallelopiped of length 5 m is divided internally by a movable partition P as shown in the figure. The left compartment is filled with a given mass of an ideal gas of molar mass 32 while the right compartment is filled with an equal mass of another ideal gas of molar mass 18 at same temperature. What will be the distance of P from the left wall A when equilibrium is established?

1. 2.5 m
2. 1.8 m
3. 3.2 m
4. 2.1 m

Q. One mole of an ideal monoatomic gas is heated at a constant pressure of one atmosphere from $0^{\circ }$C to ${100}^{\circ }$ C. Then the change in the internal energy is

1. 20.80 joules
2. 6.56 joules
3. 
4. 

Q. If the rms speed of oxygen molecules at $0^{\circ }\text{C}$ is $160\text{m/s}$, find the rms speed of hydrogen molecules at $0^{\circ }\text{C}$.

1. $80\text{m/s}$
2. $640\text{m/s}$
3. $40\text{m/s}$
4. $332\text{m/s}$

Q. One $\text{mole}$ of an ideal monoatomic gas is taken at a temperature of $300\text{K}$. If the volume is doubled keeping its pressure constant, change in internal energy is

1. $450R$
2. $600R$
3. $500R$
4. $400R$

Q. A triatomic, diatomic and monoatomic gas are supplied with the same amount of heat at a constant pressure. Then:

1. Fraction of energy used to change internal energy for maximum in monoatomic gas.
2. Fraction of energy used to change internal energy is maximum for diatomic gas.
3. Fraction of energy used to change internal energy is maximum for triatomic gas.
4. Fraction of energy used to change internal energy is same for all the three gases.

Q.

A particle is fired upward with a speed of 20 km/s. The speed with which it will move in interstellar space is

1. 8.8 km/s

2. 16.5 km/s

3. 11.2 km/s

4. 10 km/s

Q. Find the change in internal energy of $3\text{mol}$ of helium gas when its temperature is increased by $2\text{K}$.

1. $7.48\text{J}$
2. $12\text{J}$
3. $74.8\text{J}$
4. $74.8\text{cal}$

Q.

What is the symbol for SI unit of mole and how is it defined?

Q. In the following figures (a) to (d), variation of volume with change of pressure along the path ABCDA is shown. Change in internal energy of the gas will be -

1. positive in cases (a), (b) and (c), but zero in case (d)
2. negative in cases (a), (b) and (c), but zero in case (d)
3. positive in all cases from (a) to (d)
4. zero in all the four cases

Q.

If the potential energy of a gas molecule is

U= M/r^{​​​​​​6} - N/r^{​​​​​​12}

M&N being positive constant, then the potential energy at equilibrium must be

a: zero. b: M²/4N. c:NM^{​​​​​2}/4. d:MN​​​​​​​​²/4

Q. A gas mixture consists of 2 moles of oxygen and 4 moles of Argon at temperature $T$. Neglecting all vibrational degrees of freedom, the total internal energy of the system is

1. $4RT$
2. $15RT$
3. $9RT$
4. $11RT$

Q. The average kinetic energy per molecule of helium gas at temperature T is E and the molar gas constant is R, then Avogadro’s number is

1. 
   
   
2. 
   
3. 
   
   
4. 
   
   

Q.

The visible universe is estimated to contain ${10}^{22}$stars. How many moles are present in the visible universe?

Q. If 2 moles of an ideal monoatomic gas at temperature $T_0$ is mixed with 4 moles of another ideal monoatomic gas at temperature $2T_0$ in a closed vessel, then the temperature of the mixture is

1. $\frac{5}{3}{T}_0$
2. $\frac{3}{2}{T}_0$
3. $\frac{4}{3}{T}_0$
4. $\frac{5}{4}{T}_0$

Q. A mixture of $10\text{g}$ of hydrogen and $40\text{g}$ of helium are kept in a closed vessel. To change the temperature of the mixture by ${50}^{\circ }\text{C}$, the amount of heat energy should be added to the mixture is
(Given $R=2{\text{cal mol}}^{-1}{}^{\circ }{\text{C}}^{-1}$)

1. $2500\text{cal}$
2. $2750\text{cal}$
3. $2000\text{cal}$
4. None of these

Q. The change in internal energy of two moles of a monoatomic gas, when the temperature increases by ${50}^{\circ }\text{C}$ is
[Take $R=2{\text{cal mol}}^{-1}{}^{\circ }{\text{C}}^{-1}$]

1. $1251\text{J}$
2. $300\text{cal}$
3. $1251\text{cal}$
4. $300\text{J}$

Q. One Quantum is observed for gaseous molecules of br2 for converting into br atoms if light observed has the wavelenth 5000 Armstrong calculate energy required in kilojoule mol

Q. Why the internal energy of a monatomic ideal gas molecule is totally Kinetic

Q. Find the molar specific heat (in $\text{J mol}{}^{-1}\text{K}{}^{-1}$) for a process where $P=\frac{a}{T}$, for one mole of a monatomic gas, ${}^{\prime }{a}^{\prime }$ being constant.

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

Q.

Calculate the ratio of atoms present in $5\mathrm{g}$of magnesium and $5g$of iron (Atomic Mass $\mathrm{Mg}=24,\mathrm{Fe}=56$).

Q. One gram of ice at $0^{\circ }$C is mixed with one gram of steam at ${100}^{\circ }$C . At thermal equilibrium the temperature of mixture is

1. 100°C
2. 0°C
3. 55°C
4. 80°C

Q.

A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m²s^–2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a magnitude 4.2 α^–1 β^–2 γ² in terms of the new units.

Q. A proton and an alpha particle are accelerating by the same potential difference. Find the ratio of their de-Broglie wavelength? $\left(\text{charge}\right(q_{\alpha })=+2e,q_{proton}=+e\text{and}{m}_{\alpha }=4m_{proton})$

1. $\sqrt{2}$
2. $\sqrt{8}$
3. $\sqrt{6}$
4. $\sqrt{16}$