Thermodynamics Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. The relation between U, P and V for an ideal gas in an adiabatic process
is given by relation U = a + bP V. Find the value of adiabatic exponent
(?) of this gas
(a)
(b)
(c)
(d)
2. Carbon monoxide is carried around a closed cycle abc in which bc is an
isothermal process as shown in the figure. The gas absorbs 7000 J of
heat as its temperture increases from 300 K to 1000 K in going from a
to b. The quantity of heat rejected by the gas during the process ca is
Page 2


PART-I (Single Correct MCQs)
1. The relation between U, P and V for an ideal gas in an adiabatic process
is given by relation U = a + bP V. Find the value of adiabatic exponent
(?) of this gas
(a)
(b)
(c)
(d)
2. Carbon monoxide is carried around a closed cycle abc in which bc is an
isothermal process as shown in the figure. The gas absorbs 7000 J of
heat as its temperture increases from 300 K to 1000 K in going from a
to b. The quantity of heat rejected by the gas during the process ca is
(a) 4200 J
(b) 5000 J
(c) 9000 J
(d) 9800 J
3. An insulated container of gas has two chambers
separated by an insulating partition. One of the
chambers has volume V
1
 and  contains ideal gas
at pressure P
1
 and temperature T
1
. The other
chamber has volume V
2
 and contains ideal gas at
pressure P
2
 and temperature T
2
. If the partition is
removed without doing any work on the gas, the
final equilibrium temperature of the gas in the container will be
(a)
(b)
(c)
(d)
4. Consider a spherical shell of radius R at temperature T. The black body
radiation inside it can be considered as an ideal gas of photons with
internal energy per unit volume u =  ? T
4
 and pressure . If
the shell now undergoes an adiabatic expansion the relation between T
and R is :
(a)
Page 3


PART-I (Single Correct MCQs)
1. The relation between U, P and V for an ideal gas in an adiabatic process
is given by relation U = a + bP V. Find the value of adiabatic exponent
(?) of this gas
(a)
(b)
(c)
(d)
2. Carbon monoxide is carried around a closed cycle abc in which bc is an
isothermal process as shown in the figure. The gas absorbs 7000 J of
heat as its temperture increases from 300 K to 1000 K in going from a
to b. The quantity of heat rejected by the gas during the process ca is
(a) 4200 J
(b) 5000 J
(c) 9000 J
(d) 9800 J
3. An insulated container of gas has two chambers
separated by an insulating partition. One of the
chambers has volume V
1
 and  contains ideal gas
at pressure P
1
 and temperature T
1
. The other
chamber has volume V
2
 and contains ideal gas at
pressure P
2
 and temperature T
2
. If the partition is
removed without doing any work on the gas, the
final equilibrium temperature of the gas in the container will be
(a)
(b)
(c)
(d)
4. Consider a spherical shell of radius R at temperature T. The black body
radiation inside it can be considered as an ideal gas of photons with
internal energy per unit volume u =  ? T
4
 and pressure . If
the shell now undergoes an adiabatic expansion the relation between T
and R is :
(a)
(b)
(c) T ? e
–R
(d) T ? e
–3R
5. A refrigerator works between 4°C and 30°C. It is required to remove
600 calories of heat every second in order to keep the temperature of
the refrigerated space constant. The power required is: (Take 1 cal = 4.2
joule)
(a) 2.365 W (b) 23.65 W (c) 236.5 W (d) 2365 W
6. A system goes from A to B via two processes I
and II as shown in figure. If ?U
1
 and ?U
2
 are the
changes in internal energies in the processes I and
II respectively, then the relation between ?U
1
 and
?U
2 
is
(a) ?U
1
 = ?U
2
(b) ?U
2
 < ?U
1
(c) ?U
2
 > ?U
1
(d) can not be determined
7. A diatomic ideal gas is used in a Carnot engine as the working
substance. If during the adiabatic expansion part of the cycle the
volume of the gas increases from V to 32 V, the efficiency of the engine
?
(a) 0.5
(b) 0.75
(c) 0.99
(d) 0.25
8. ‘n’ moles of an ideal gas undergoes a process A ? B as shown in the
figure. The maximum temperature of the gas during the process will be
:
Page 4


PART-I (Single Correct MCQs)
1. The relation between U, P and V for an ideal gas in an adiabatic process
is given by relation U = a + bP V. Find the value of adiabatic exponent
(?) of this gas
(a)
(b)
(c)
(d)
2. Carbon monoxide is carried around a closed cycle abc in which bc is an
isothermal process as shown in the figure. The gas absorbs 7000 J of
heat as its temperture increases from 300 K to 1000 K in going from a
to b. The quantity of heat rejected by the gas during the process ca is
(a) 4200 J
(b) 5000 J
(c) 9000 J
(d) 9800 J
3. An insulated container of gas has two chambers
separated by an insulating partition. One of the
chambers has volume V
1
 and  contains ideal gas
at pressure P
1
 and temperature T
1
. The other
chamber has volume V
2
 and contains ideal gas at
pressure P
2
 and temperature T
2
. If the partition is
removed without doing any work on the gas, the
final equilibrium temperature of the gas in the container will be
(a)
(b)
(c)
(d)
4. Consider a spherical shell of radius R at temperature T. The black body
radiation inside it can be considered as an ideal gas of photons with
internal energy per unit volume u =  ? T
4
 and pressure . If
the shell now undergoes an adiabatic expansion the relation between T
and R is :
(a)
(b)
(c) T ? e
–R
(d) T ? e
–3R
5. A refrigerator works between 4°C and 30°C. It is required to remove
600 calories of heat every second in order to keep the temperature of
the refrigerated space constant. The power required is: (Take 1 cal = 4.2
joule)
(a) 2.365 W (b) 23.65 W (c) 236.5 W (d) 2365 W
6. A system goes from A to B via two processes I
and II as shown in figure. If ?U
1
 and ?U
2
 are the
changes in internal energies in the processes I and
II respectively, then the relation between ?U
1
 and
?U
2 
is
(a) ?U
1
 = ?U
2
(b) ?U
2
 < ?U
1
(c) ?U
2
 > ?U
1
(d) can not be determined
7. A diatomic ideal gas is used in a Carnot engine as the working
substance. If during the adiabatic expansion part of the cycle the
volume of the gas increases from V to 32 V, the efficiency of the engine
?
(a) 0.5
(b) 0.75
(c) 0.99
(d) 0.25
8. ‘n’ moles of an ideal gas undergoes a process A ? B as shown in the
figure. The maximum temperature of the gas during the process will be
:
(a)
(b)
(c)
(d)
9. The volume of an ideal gas is 1 litre and its pressure is equal to 72 cm
of mercury column. The volume of gas is made900 cm
3
 by compressing
it isothermally. The stress of the gas will be
(a) 8 cm of Hg
(b) 7 cm of Hg
(c) 6 cm of Hg
(d) 4 cm of Hg
10. A diatomic gas initally at 18ºC is compressed adiabatically to one
eighth of its original volume. The temperature after compression will be
(a) 18ºC
(b) 887ºC
(c) 327ºC
(d) 395.5°C
11. An ideal gas goes from state A to state B via
three different processes as indicated in the P-V
diagram :
If Q
1
, Q
2
, Q
3
 indicate the heat a absorbed by the gas
along the three processes and ?U
1
, ?U
2
, ?U
3
indicate the change in internal energy along the
three processes respectively, then
Page 5


PART-I (Single Correct MCQs)
1. The relation between U, P and V for an ideal gas in an adiabatic process
is given by relation U = a + bP V. Find the value of adiabatic exponent
(?) of this gas
(a)
(b)
(c)
(d)
2. Carbon monoxide is carried around a closed cycle abc in which bc is an
isothermal process as shown in the figure. The gas absorbs 7000 J of
heat as its temperture increases from 300 K to 1000 K in going from a
to b. The quantity of heat rejected by the gas during the process ca is
(a) 4200 J
(b) 5000 J
(c) 9000 J
(d) 9800 J
3. An insulated container of gas has two chambers
separated by an insulating partition. One of the
chambers has volume V
1
 and  contains ideal gas
at pressure P
1
 and temperature T
1
. The other
chamber has volume V
2
 and contains ideal gas at
pressure P
2
 and temperature T
2
. If the partition is
removed without doing any work on the gas, the
final equilibrium temperature of the gas in the container will be
(a)
(b)
(c)
(d)
4. Consider a spherical shell of radius R at temperature T. The black body
radiation inside it can be considered as an ideal gas of photons with
internal energy per unit volume u =  ? T
4
 and pressure . If
the shell now undergoes an adiabatic expansion the relation between T
and R is :
(a)
(b)
(c) T ? e
–R
(d) T ? e
–3R
5. A refrigerator works between 4°C and 30°C. It is required to remove
600 calories of heat every second in order to keep the temperature of
the refrigerated space constant. The power required is: (Take 1 cal = 4.2
joule)
(a) 2.365 W (b) 23.65 W (c) 236.5 W (d) 2365 W
6. A system goes from A to B via two processes I
and II as shown in figure. If ?U
1
 and ?U
2
 are the
changes in internal energies in the processes I and
II respectively, then the relation between ?U
1
 and
?U
2 
is
(a) ?U
1
 = ?U
2
(b) ?U
2
 < ?U
1
(c) ?U
2
 > ?U
1
(d) can not be determined
7. A diatomic ideal gas is used in a Carnot engine as the working
substance. If during the adiabatic expansion part of the cycle the
volume of the gas increases from V to 32 V, the efficiency of the engine
?
(a) 0.5
(b) 0.75
(c) 0.99
(d) 0.25
8. ‘n’ moles of an ideal gas undergoes a process A ? B as shown in the
figure. The maximum temperature of the gas during the process will be
:
(a)
(b)
(c)
(d)
9. The volume of an ideal gas is 1 litre and its pressure is equal to 72 cm
of mercury column. The volume of gas is made900 cm
3
 by compressing
it isothermally. The stress of the gas will be
(a) 8 cm of Hg
(b) 7 cm of Hg
(c) 6 cm of Hg
(d) 4 cm of Hg
10. A diatomic gas initally at 18ºC is compressed adiabatically to one
eighth of its original volume. The temperature after compression will be
(a) 18ºC
(b) 887ºC
(c) 327ºC
(d) 395.5°C
11. An ideal gas goes from state A to state B via
three different processes as indicated in the P-V
diagram :
If Q
1
, Q
2
, Q
3
 indicate the heat a absorbed by the gas
along the three processes and ?U
1
, ?U
2
, ?U
3
indicate the change in internal energy along the
three processes respectively, then
(a) Q
1 
>  Q
2 
>  Q
3
 and ?U
1 
= ?U
2 
= ?U
3
(b) Q
3 
>  Q
2 
> Q
1
 and ?U
1
= ?U
2 
= ?U
3
(c) Q
1 
=  Q
2 
= Q
3
 and ?U
1 
> ?U
2 
> ?U
3
(d) Q
3 
> Q
2 
> Q
1
 and ?U
1
> ?U
2 
> ?U
3
12. In a thermodynamic process, fixed mass of a gas is changed in such a
manner that the gas release 20 J of heat and 8 J of work was done on the
gas. If the initial internal energy of the gas was 30 J, the final internal
energy will be
(a) 2 joule
(b) 18 joule
(c) 42 joule
(d) 58 joule
13. In a Carnot engine, the temperature of reservoir is 927°C and that of
sink is 27°C. If the work done by the engine when it transfers heat from
reservoir to sink is 12.6 × 10
6
J, the quantity of heat absorbed by the
engine from the reservoir is
(a) 16.8 × 10
6
 J
(b) 4 × 10
6
 J
(c) 7.6 × 10
6
 J
(d) 4.2 × 10
6
 J
14. 5.6 litre of helium gas at STP is adiabatically compressed to 0.7 litre.
Taking the initial temperature to be T
1
, the work done in the process is
(a)
(b)
(c)