Kinetic Theory Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. Air is pumped into an automobile tube upto a pressure of 200 kPa in the
morning when the air temperature is 22°C. During the day, temperature
rises to 42°C and the tube expands by 2%. The pressure of the air in the
tube at this temperature, will be approximately
(a) 212 kPa
(b) 209 kPa
(c) 206 kPa
(d) 200 kPa
2. 4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of
the gas at constant volume is 5.0JK
–1
. If the speed of any quantity x in
this gas at NTP is 952 ms
–1
, then the heat capacity at constant pressure
is (Take gas constant R = 8.3 JK
–1
 mol
–1
)
(a) 7.5 JK
–1
 mol
–1
(b) 7.0 JK
–1
 mol
–1
(c) 8.5 JK
–1
 mol
–1
Page 2


PART-I (Single Correct MCQs)
1. Air is pumped into an automobile tube upto a pressure of 200 kPa in the
morning when the air temperature is 22°C. During the day, temperature
rises to 42°C and the tube expands by 2%. The pressure of the air in the
tube at this temperature, will be approximately
(a) 212 kPa
(b) 209 kPa
(c) 206 kPa
(d) 200 kPa
2. 4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of
the gas at constant volume is 5.0JK
–1
. If the speed of any quantity x in
this gas at NTP is 952 ms
–1
, then the heat capacity at constant pressure
is (Take gas constant R = 8.3 JK
–1
 mol
–1
)
(a) 7.5 JK
–1
 mol
–1
(b) 7.0 JK
–1
 mol
–1
(c) 8.5 JK
–1
 mol
–1
(d) 8.0 JK
–1
 mol
–1
3. The figure shows the volume V versus temperature T
graphs for a certain mass of a perfect gas at two
constant pressures of P
1
 and P
2
. What inference can
you draw from the graphs?
(a) P
1
 > P
2
(b) P
1
 < P
2
(c) P
1
 = P
2
(d) No inference can be drawn due to insufficient information.
4. Consider an ideal gas confined in an isolated closed chamber. As the
gas undergoes an adiabatic expansion, the average time of collision
between molecules increases as V
q
, where V is the volume of the gas.
The value of q is : 
(a)
(b)
(c)
(d)
5. Work done by a system under isothermal change from a volume V
1
 to
V
2
 for a gas which obeys Vander Waal’s equation 
is
(a)
(b)
Page 3


PART-I (Single Correct MCQs)
1. Air is pumped into an automobile tube upto a pressure of 200 kPa in the
morning when the air temperature is 22°C. During the day, temperature
rises to 42°C and the tube expands by 2%. The pressure of the air in the
tube at this temperature, will be approximately
(a) 212 kPa
(b) 209 kPa
(c) 206 kPa
(d) 200 kPa
2. 4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of
the gas at constant volume is 5.0JK
–1
. If the speed of any quantity x in
this gas at NTP is 952 ms
–1
, then the heat capacity at constant pressure
is (Take gas constant R = 8.3 JK
–1
 mol
–1
)
(a) 7.5 JK
–1
 mol
–1
(b) 7.0 JK
–1
 mol
–1
(c) 8.5 JK
–1
 mol
–1
(d) 8.0 JK
–1
 mol
–1
3. The figure shows the volume V versus temperature T
graphs for a certain mass of a perfect gas at two
constant pressures of P
1
 and P
2
. What inference can
you draw from the graphs?
(a) P
1
 > P
2
(b) P
1
 < P
2
(c) P
1
 = P
2
(d) No inference can be drawn due to insufficient information.
4. Consider an ideal gas confined in an isolated closed chamber. As the
gas undergoes an adiabatic expansion, the average time of collision
between molecules increases as V
q
, where V is the volume of the gas.
The value of q is : 
(a)
(b)
(c)
(d)
5. Work done by a system under isothermal change from a volume V
1
 to
V
2
 for a gas which obeys Vander Waal’s equation 
is
(a)
(b)
(c)
(d)
6. A thermally insulated vessel contains an ideal gas of molecular mass M
and ratio of specific heats ?. It is moving with speed v and it suddenly
brought to rest. Assuming no heat is lost to the surroundings, its
temperature increases by
(a)
(b)
(c)
(d)
7. The temperature at which proton in hydrogen gas would have enough
energy to overcome a barrier of 4.14 × 10
–14
 J is
(Boltzmann constant = 1.38 × 10
–23
 JK
–1
)
(a) 2 × 10
9
 K (b) 10
9
 K (c) 6 × 10
9
 K (d) 3 × 10
9
 K
8. If 2 moles of an ideal monatomic gas at temperature T
0
 is mixed with 4
moles of another ideal monatomic gas at temperature 2T
0
, then the
temperature of the mixture is
(a)
(b)
(c)
(d)
Page 4


PART-I (Single Correct MCQs)
1. Air is pumped into an automobile tube upto a pressure of 200 kPa in the
morning when the air temperature is 22°C. During the day, temperature
rises to 42°C and the tube expands by 2%. The pressure of the air in the
tube at this temperature, will be approximately
(a) 212 kPa
(b) 209 kPa
(c) 206 kPa
(d) 200 kPa
2. 4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of
the gas at constant volume is 5.0JK
–1
. If the speed of any quantity x in
this gas at NTP is 952 ms
–1
, then the heat capacity at constant pressure
is (Take gas constant R = 8.3 JK
–1
 mol
–1
)
(a) 7.5 JK
–1
 mol
–1
(b) 7.0 JK
–1
 mol
–1
(c) 8.5 JK
–1
 mol
–1
(d) 8.0 JK
–1
 mol
–1
3. The figure shows the volume V versus temperature T
graphs for a certain mass of a perfect gas at two
constant pressures of P
1
 and P
2
. What inference can
you draw from the graphs?
(a) P
1
 > P
2
(b) P
1
 < P
2
(c) P
1
 = P
2
(d) No inference can be drawn due to insufficient information.
4. Consider an ideal gas confined in an isolated closed chamber. As the
gas undergoes an adiabatic expansion, the average time of collision
between molecules increases as V
q
, where V is the volume of the gas.
The value of q is : 
(a)
(b)
(c)
(d)
5. Work done by a system under isothermal change from a volume V
1
 to
V
2
 for a gas which obeys Vander Waal’s equation 
is
(a)
(b)
(c)
(d)
6. A thermally insulated vessel contains an ideal gas of molecular mass M
and ratio of specific heats ?. It is moving with speed v and it suddenly
brought to rest. Assuming no heat is lost to the surroundings, its
temperature increases by
(a)
(b)
(c)
(d)
7. The temperature at which proton in hydrogen gas would have enough
energy to overcome a barrier of 4.14 × 10
–14
 J is
(Boltzmann constant = 1.38 × 10
–23
 JK
–1
)
(a) 2 × 10
9
 K (b) 10
9
 K (c) 6 × 10
9
 K (d) 3 × 10
9
 K
8. If 2 moles of an ideal monatomic gas at temperature T
0
 is mixed with 4
moles of another ideal monatomic gas at temperature 2T
0
, then the
temperature of the mixture is
(a)
(b)
(c)
(d)
9. For a gas, difference between two specific heats is 5000 J/mole°C. If
the ratio of specific heats is 1.6, the two specific heats in J/mole-°C are
(a) C
P
 = 1.33 × 10
4
, C
V
 = 2.66 × 10
4
(b) C
P
 = 13.3 × 10
4
, C
V
 = 8.33 × 10
3
(c) C
P
 = 1.33 × 10
4
, C
V
 = 8.33 × 10
3
(d) C
P
 = 2.6 × 10
4
, C
V
 = 8.33 × 10
4
10. A graph is plotted with PV/T on y-axis and mass of the gas along x-axis
for different gases. The graph is
(a) a straight line parallel to x-axis for all the gases
(b) a straight line passing through origin with a slope having a constant
value for all the gases
(c) a straight line passing through origin with a slope having different
values for different gases
(d) a straight line parallel to y-axis for all the gases
11. One mole of a gas occupies 22.4 lit at N.T.P. Calculate the difference
between two molar specific heats of the gas.
J = 4200 J/kcal.
(a) 1.979 k cal/kmol K
(b) 2.378 k cal/kmol K
(c) 4.569 kcal/kmol K (d) 3.028 k cal/ kmol K
12. The temperature of the mixture of one mole of helium and one mole of
hydrogen is increased from 0°C to 100°C at constant pressure. The
amount of heat delivered will be
(a) 600 cal
(b) 1200 cal
(c) 1800 cal
(d) 3600 cal
13. The P-V diagram of a diatomic gas is a straight line passing through
origin. The molar heat capacity of the gas in the process will be
(a) 4 R
Page 5


PART-I (Single Correct MCQs)
1. Air is pumped into an automobile tube upto a pressure of 200 kPa in the
morning when the air temperature is 22°C. During the day, temperature
rises to 42°C and the tube expands by 2%. The pressure of the air in the
tube at this temperature, will be approximately
(a) 212 kPa
(b) 209 kPa
(c) 206 kPa
(d) 200 kPa
2. 4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of
the gas at constant volume is 5.0JK
–1
. If the speed of any quantity x in
this gas at NTP is 952 ms
–1
, then the heat capacity at constant pressure
is (Take gas constant R = 8.3 JK
–1
 mol
–1
)
(a) 7.5 JK
–1
 mol
–1
(b) 7.0 JK
–1
 mol
–1
(c) 8.5 JK
–1
 mol
–1
(d) 8.0 JK
–1
 mol
–1
3. The figure shows the volume V versus temperature T
graphs for a certain mass of a perfect gas at two
constant pressures of P
1
 and P
2
. What inference can
you draw from the graphs?
(a) P
1
 > P
2
(b) P
1
 < P
2
(c) P
1
 = P
2
(d) No inference can be drawn due to insufficient information.
4. Consider an ideal gas confined in an isolated closed chamber. As the
gas undergoes an adiabatic expansion, the average time of collision
between molecules increases as V
q
, where V is the volume of the gas.
The value of q is : 
(a)
(b)
(c)
(d)
5. Work done by a system under isothermal change from a volume V
1
 to
V
2
 for a gas which obeys Vander Waal’s equation 
is
(a)
(b)
(c)
(d)
6. A thermally insulated vessel contains an ideal gas of molecular mass M
and ratio of specific heats ?. It is moving with speed v and it suddenly
brought to rest. Assuming no heat is lost to the surroundings, its
temperature increases by
(a)
(b)
(c)
(d)
7. The temperature at which proton in hydrogen gas would have enough
energy to overcome a barrier of 4.14 × 10
–14
 J is
(Boltzmann constant = 1.38 × 10
–23
 JK
–1
)
(a) 2 × 10
9
 K (b) 10
9
 K (c) 6 × 10
9
 K (d) 3 × 10
9
 K
8. If 2 moles of an ideal monatomic gas at temperature T
0
 is mixed with 4
moles of another ideal monatomic gas at temperature 2T
0
, then the
temperature of the mixture is
(a)
(b)
(c)
(d)
9. For a gas, difference between two specific heats is 5000 J/mole°C. If
the ratio of specific heats is 1.6, the two specific heats in J/mole-°C are
(a) C
P
 = 1.33 × 10
4
, C
V
 = 2.66 × 10
4
(b) C
P
 = 13.3 × 10
4
, C
V
 = 8.33 × 10
3
(c) C
P
 = 1.33 × 10
4
, C
V
 = 8.33 × 10
3
(d) C
P
 = 2.6 × 10
4
, C
V
 = 8.33 × 10
4
10. A graph is plotted with PV/T on y-axis and mass of the gas along x-axis
for different gases. The graph is
(a) a straight line parallel to x-axis for all the gases
(b) a straight line passing through origin with a slope having a constant
value for all the gases
(c) a straight line passing through origin with a slope having different
values for different gases
(d) a straight line parallel to y-axis for all the gases
11. One mole of a gas occupies 22.4 lit at N.T.P. Calculate the difference
between two molar specific heats of the gas.
J = 4200 J/kcal.
(a) 1.979 k cal/kmol K
(b) 2.378 k cal/kmol K
(c) 4.569 kcal/kmol K (d) 3.028 k cal/ kmol K
12. The temperature of the mixture of one mole of helium and one mole of
hydrogen is increased from 0°C to 100°C at constant pressure. The
amount of heat delivered will be
(a) 600 cal
(b) 1200 cal
(c) 1800 cal
(d) 3600 cal
13. The P-V diagram of a diatomic gas is a straight line passing through
origin. The molar heat capacity of the gas in the process will be
(a) 4 R
(b) 2.5 R
(c) 3 R
(d)
14. 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)
(b)
(c)
(d)
15. A sample of an ideal gas occupies a volume V at a pressure P and
absolute temperature T. The mass of each molecule is m. The equation
for density is
(a) m k T
(b) P/k T
(c) P/(k T V)
(d) P m/k T
16. A vessel has 6g of hydrogen at pressure P and temperature 500K. A
small hole is made in it so that hydrogen leaks out.   How much
hydrogen leaks out if the final pressure is P/2 and temperature falls to
300 K ?
(a) 2g
(b) 3g