Kinetic theory of gases

1.

Two thermally insulated vessels $1$ and $2$ are filled with air at temperatures $\mathrm{T_1},$ $\mathrm{T_2},$ volume $\mathrm{V_1},$ $\mathrm{V_2}$ and pressure $\mathrm{P_1},$ $\mathrm{P_2}$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be:

1.	$T_1+T_2$	2.	$\dfrac{T_1+T_2}{2}$
3.	$\dfrac{T_1T_2(P_1V_1+P_2V_2)}{P_1V_1T_2+P_2V_2T_1}$	4.	$\dfrac{T_1T_2(P_1V_1+P_2V_2)}{P_1V_1T_1+P_2V_2T_2}$

2.

In Vander Waal’s equation, a and b represent $(P + \frac{a}{V^{2}}) (v - b) = RT$
1. Both a and b represent correction in volume
2. Both a and b represent adhesive force between molecules
3. a represents adhesive force between molecules and b correction in volume
4. a represents correction in volume and b represents adhesive force between molecules

3.

The maximum attainable temperature of ideal gas in the process $P = P_{0} - {αV}^{2}$ where $P_{0}$ and $α$ are +ve constants
1. $\frac{2 P_{0}}{3 nR} {(\frac{P_{0}}{3 α})}^{1 / 2}$
2. $\frac{P_{0}}{2 nR} {(\frac{2 P_{0}}{3 α})}^{1 / 2}$
3. $\frac{2 nR}{P_{0}} {(\frac{2 P_{0}}{3 α})}^{1 / 2}$
4. $\frac{2 P_{0}}{nR} {(\frac{P_{0}}{2 α})}^{1 / 2}$

4.

Two different isotherms representing the relationship between pressure $P$ and volume $V$ at a given temperature of the same ideal gas are shown for masses $m_1$ and $m_2,$ then:

1.	nothing can be predicted
2.	$m_1 < m_2$
3.	$m_1 = m_2$
4.	$m_1 > m_2$

5.

Two identical glass bulbs are interconnected by a thin glass tube. A gas is filled in these bulbs at N.T.P. If one bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes 1.5 times. The temperature of hot bath will be

1. 100°C
2. 182°C
3. 256°C
4. 546°C

6.

Consider a 1 c.c. sample of air at the absolute temperature $T_{0}$ at sea level and another 1 c.c. sample of air at a height where the pressure is the one-third atmosphere. The absolute temperature T of the sample at that height is :
1. Equal to $T_{0} / 3$
2. Equal to $3 / T_{0}$
3. Equal to $T_{0}$
4. Cannot be determined in terms of $T_{0}$ from the above data

7.

Which one of the following graph is correct at constant pressure?

1.		2.
3.		4.

8.

If at a pressure of $10^6$ dyne/cm², one gram of nitrogen occupies $2\times10^4$c.c. volume, then the average energy of a nitrogen molecule in erg is:

1.	$14\times10^{-13}$	2.	$10\times10^{-12}$
3.	$10^{6}$	4.	$2\times10^{6}$

9.

Maxwell's velocity distribution curve is given for two different temperatures. For the given curves-

1. $T_{1} > T_{2}$
2. $T_{1} < T_{2}$
3. $T_{1} \leq T_{2}$
4. $T_{1} = T_{2}$

10.

If the ratio of vapour density for hydrogen and oxygen is $\frac{1}{16},$ then under constant pressure, the ratio of their RMS velocities will be:

1.	$\frac{4}{1}$	2.	$\frac{1}{4}$
3.	$\frac{1}{16}$	4.	$\frac{16}{1}$

11.

Figure shows a parabolic graph between T and 1/V for a mixture of a gas undergoing an adiabatic process. What is the ratio of V_rms of molecules and speed of sound in mixture ?

1. $\sqrt{3 / 2}$
2. $\sqrt{2}$
3. $\sqrt{2 / 3}$
4. $\sqrt{3}$

12.

The molecules of a given mass of a gas have a r.m.s. velocity of 200 m/sec at 27°C and $1.0 \times 10^{5} N / m^{2}$ pressure. When the temperature is 127°C and pressure is $0.5 \times 10^{5} N / m^{2},$ the r.m.s. velocity in m/sec will be
1. $\frac{100 \sqrt{2}}{3}$
2. $100 \sqrt{2}$
3. $\frac{400}{\sqrt{3}}$
4. None of the above

13.

The temperature of a gas is - $68 ° C$ . At what temperature will the average kinetic energy of its molecules be twice that of $68 ° C$ ?
1.   $137 ° C$
2.   $127 ° C$
3.   $100 ° C$
4.   $105 ° C$

14.

If the mean free path of atoms is doubled, then the pressure of the gas will become:
1. $\frac{P}{4}$
2. $\frac{P}{2}$
3. $\frac{P}{8}$
4. $P$

15.

The specific heat at constant volume of mixture of $N_{2}$ and He will be (moles are same):
1. 3R
2. 1.5R
3. 1.9R
4. 2R

16.

$C_{p}$ and $C_{v}$ are specific heats at constant pressure and constant volume respectively. It is observed that
$C_{p}$ - $C_{v}$ = a for hydrogen gas
$C_{p}$ - $C_{v}$ = b for nitrogen gas
The correct relation between a and b is :
1. a = 14 b
2. a = 28 b
3. $a = \frac{1}{14} b$
4. a = b

17.

The specific heat of a gas:

1.	has only two values $Cp$ and $Cv$.
2.	has a unique value at a given temperature.
3.	can have any value between 0 and ∞.
4.	depends upon the mass of the gas.

18.

When the temperature of a gas increases by 1 $°$ C, its pressure increases by 0.4%. What is its initial temperature?
1. 250 K
2. 240 K
3. 210 K
4. 200 K

19.

Six molecules have speeds 2 units, 5 units, 3 units, 6 units, 3 units, d 5 units respectively. The RMS speed is :
1. 4 unit
2. 1.7 unit
3. 4.2 unit
4. 5 unit

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1.	\(T_1+T_2\)	2.	\(\dfrac{T_1+T_2}{2}\)
3.	\(\dfrac{T_1T_2(P_1V_1+P_2V_2)}{P_1V_1T_2+P_2V_2T_1}\)	4.	\(\dfrac{T_1T_2(P_1V_1+P_2V_2)}{P_1V_1T_1+P_2V_2T_2}\)

1.	nothing can be predicted
2.	\(m_1 < m_2\)
3.	\(m_1 = m_2\)
4.	\(m_1 > m_2\)

1.	\(14\times10^{-13}\)	2.	\(10\times10^{-12}\)
3.	\(10^{6}\)	4.	\(2\times10^{6}\)

1.	\(\frac{4}{1}\)	2.	\(\frac{1}{4}\)
3.	\(\frac{1}{16}\)	4.	\(\frac{16}{1}\)

1.	has only two values \(Cp\) and \(Cv\).
2.	has a unique value at a given temperature.
3.	can have any value between 0 and ∞.
4.	depends upon the mass of the gas.

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