HEAT REVISION (i10,i11)
1.
2.
A gas of temperature T is enclosed in a container whose walls are (initially) at
temperature T1. Does the gas exert a higher pressure on the walls of the
container when T1 < T or when T1 > T?
Consider two identical iron spheres, one of which lies on a thermally
insulating plate, whilst the other hangs from an insulating thread.
Equal amounts of heat are given to the two spheres. Which will have the
higher temperature?
5.
n moles of a monoatomic gas at temperature T1 are trapped under a piston
having area A, length
, density  and thermal conductivity K. P0 and T0 are
pressure and temperature of the atmosphere. Find length of the gas column
as a function of time. Neglect friction and heat loss through the walls of
container and sides of piston.
9.
An adiabatic cylinder of length 1 m and area of cross section 102 m2 is closed
at both ends. A freely moving nonconducting thin piston divides the cylinder
into two equal parts. Each part contains 28 gm of N2 . The natural length of
the spring connected to the piston and right wall of the cylinder is =50 cm
N
1
and k  2 103
. Initially rd molecules of the nitrogen in the right part
m
3
are dissociated into atoms. If initial pressure in each part is
P0  2 105 N/m2 calculate,
a) work done by the gas in right part
b) the heat supplied by the heater to compress the spring by
3
.
4
10.
An ideal monoatomic gas is taken through the following cycle: linear
expansion from a state  P0 ,V0 ,T0  to a state  P1,V1, T1  followed by an adiabatic
compression back to the original state. Given that P0  32,V0  8,P1  1 and
V1  64 in SI units. Calculate the thermal efficiency of the cycle.
11.
Two moles of a monoatomic ideal gas undergo a cyclic process ABCDA as
shown in figure. BCD is a semicircle. Find the efficiency of the cycle.
13.
A solid cylindrical rod of length L 0 and cross-sectional area A lies with its axis
along the x-axis and one of its ends at the origin O. The conductivity of the
material of the cylinder varies with temperature T as,
K  K 0 1  T 
If the end O is maintained at a temperature 2 T0 and the other end is at T0 .
14.
Find the rate of heat flow across the rod assuming no loss of heat from the
sides of the rods.
A horizontal insulated cylindrical vessel of length 2 is separated by a thin
insulating piston into two equal parts each of which contains n moles of an
ideal monoatomic gas at temperature T. The piston is connected to the end
faces of the vessel by undeformed springs of force constant k each. The left
part is in contact with a thermostat (a device which maintains a constant
temperature). When an amount of heat Q is supplied to the gas in the right
part, the piston is displaced to the left by a distance x  /2 . Determine the
heat Q' given away at the temperature T to the thermostat by the left part of
the piston.
16.
One end of a rod of length L and cross – sectional area A is kept in a furnace
of temperature T1. The other end of the rod is kept at a temperature T2 . The
thermal conductivity of the material of the rod is K and emissivity of the rod
is e. It is given that T2  Ts  T, where T  Ts , Ts being the temperature of the
surroundings. If T   T1  Ts  , find the proportionality constant. Consider
that heat is lost only by radiation at the end where the temperature of the rod
is T2 .
17.
The top of an insulated cylindrical container is covered by a disc having
emissivity 0.6 and conductivity 0.167 W/Km and thickness 1 cm. The
temperature is maintained by circulating oil as shown:
(a) Find the radiation loss to the surroundings in J/m2s if temperature of
the upper surface of disc is 127C and temperature of surroundings is 27C
.
(b) Also find the temperature of the circulating oil. Neglect the heat loss due
to convection.
17

8
2 4 
Given :   3  10 Wm K 


18.
A solid body X of heat capacity C is kept in an atmosphere whose temperature
is TA  300 K. At time t  0, the temperature of X is T0  400 K. It cools
according to Newton’s law of cooling. At time t1 its temperature is found to be
350 K.
At this time  t1  the body X is connected to a large body Y at atmospheric
temperature TA through a conducting rod of length L, cross-sectional area A
and thermal conductivity K. The heat capacity of Y is so large that any
variation in its temperature may be neglected. The cross-sectional area A of
the connecting rod is small compared to the surface area of X. Find the
temperature of X at time t  3t1.
19.
A horizontal frictionless piston, of negligible mass and heat capacity, divides
a vertical insulated cylinder into two halves. Each half of the cylinder contains
1 mole of air at standard temperature and pressure p 0 .
A load of weight W is now suspended from the piston, as shown in the figure.
It pulls the piston down and comes to rest after a few oscillations. How large
a volume does the compressed air in the lower part of the cylinder ultimately
occupy if W is very large?
2.
46.
Two moles of an ideal monatomic gas undergoes a cyclic process. The process
is shown on a P – V diagram, where U is the internal energy of the gas.
Calculate the net work Done.
One mole of a monoatomic ideal gas is taken through the cycle ABCDA as
shown in the figure.
Given that : TA = 1000 K, 2PA = 3PB = 6PC. Find
(i)
work done by the gas in process A  B.
(ii)
heat lost by the gas in the process B  C, and
(iii)
temperature TD.
P
A
adiabatic
B
isochoric
D
isochoric
adiabatic
V
V
P
4atm
A
B
2atm
D
13.
C
U
O
1800cal
3600cal
A vertical cylinder of uniform cross-sectional area is divided into two parts A
and B by a heavy airtight partition which can slide freely. Both chambers A
and B are filled with same gas at 300 K such that mass of gas in B is double
that of mass of gas in A and are in equilibrium, the volume of gas in A is three
times that in B. The gases on both sides are heated to the same temperature
till the partition is in equilibrium at the middle of cylinder. Calculate this
temperature.
A
B
23.
Two pieces of metals with heat capacities C1 and C2 are interconnected by a
rod of length  of uniform cross-sectional area A and low thermal conductivity
K. The temperature difference between the two pieces is 10° C at time t = 0.
Find the temperature difference between the two pieces at time t = 1 sec.
(Neglect the heat capacity of the rod)
39.
A mixture of 200 gm of water and 150 gm of ice at 0° C is kept in a calorimeter
which has water equivalent of 50 gm. If 150 gm of steam at 100° C is passed
through the mixture, calculate the final temperature and weight of the
contents of the calorimeter. Latent heat of fusion of ice = 80 cal/gm; latent
heat of vaporization of water = 540 cal/gm.
41.
For an ideal gas with adiabatic exponent , a thermodynamical cycle is shown
in V–T diagram. At state A, pressure, volume, and temperature are (Po, Vo, To).
At state B, temperature is 2To and at state C temperature is 3To. The lines AB
and CD passes through origin and the lines BC and AD are horizontal. Find
(a)
temperature at D
(b)
net heat absorbed the gas.
B
C
V
A
D
O
43.
Initial state pressure and volume of one mole of an ideal monoatomic are 3P o
and Vo respectively. Final state pressure and volume are Po and 2Vo
respectively. the gas is taken from initial state to final state through a
reversible process whose P-V diagram is represented by a straight line. Find
(a)
the heat absorbed by the gas in this process.
(b)
45.
T
the maximum temperature attained by the gas during the process.
In a process an ideal gas has a capacity of K/T, where K is a constant. Find
the amount of work done by one mole of a gas during its heating from T 1 to
T2.
50.
An ideal monoatomic gas is confined in a cylinder by a spring-loaded piston
having cross-sectional area = 8.0 × 10–3 m2. Initially, the gas is at 300 K and
occupies a volume of 2.4 × 10–3 m3 and the spring is in its released
(unstretched uncompressed) state. The gas is heated by a small electric heater
until the piston moved out slowly by 0.1 m.
Open atmosphere
Heater
Rigid
Support
Calculate the final temperature of the gas and heat supplied (in joules) by is
the heater. The force constant of the spring is 8000 N/m and the atmospheric
pressure 1.0 × 105 N/m2. The cylinder and the piston are thermally insulated.
The piston massless and there is no friction between the piston and the
cylinder. Neglect the heat loss through the lead wires of the heater. The heat
capacity of the heater is negligible. Assume the spring to be massless.
51.
Consider moles an ideal monatomic gas placed in a vertical cylinder closed by
a piston of mass M and cross-sectional area A. Initially, the gas has volume
Vo and temperature To and the piston is fixed. The piston is released and after
several oscillations come to stop.
Find the temperature and volume of the gas at equilibrium. The system is
thermally isolated, and the pressure outside the cylinder is Pa.
(Neglect the friction and heat capacity of the piston and cylinder)
M
54.
58.
Find the number (n) of strokes of a piston pump sucking in a volume 400cm3
of air during a stroke and required to pump air out of a glass flask having a
volume V = 1.0 liter to decrease its pressure to Pn = 102 Pa from initial pressure
in the flask Po = 105 Pa. The air temperature is to be considered constant.
A clock with an iron pendulum keeps correct time at 30°C. How much will it
loose or gain per day if temperature changes to 50° C. Time period at 27° C is
2 second and the coefficient of volume expansion of iron = 3 × 10–5 /°C.
60.
A one litre glass flask contains some mercury. It is found that at different
temperatures, the volume of air inside the flask remains the same. What is
the volume of mercury in this flask?
(Coefficient of linear expansion of glass = 9 × 10–6/°C and coefficient of volume
expansion of mercury = 1.8 × 10–4/°C).
78.
A body initially at 80°C cools to 64°C in 5 minutes and to 52° C in 10 minutes.
What will be its temperature after 15 minutes and what will be the
temperature of surrounding?
An ideal gas with the adiabatic exponent  undergoes a process in which its
internal energy relates to the volume as U = aV, where a and  are constants.
Find
(a)
the amount of work performed by the gas and the amount of heat to be
transferred to this gas to increase its internal energy by U,
83.
(b)
the molar heat capacity of the gas in this process.