THERMAL PROPERTIES,
THERMODYNAMICS AND KINETIC THEORY OF GAS
1. Two stars radiate maximum energy at
wavelength, 3.6 × 10–7 m and 4.8× 10–7m respectively.
What is the ratio of their temperatures? 4/3
2. A metal piece of 50 g specific heat 0.6 cal/g°C initially at 120°C is
dropped in 1.6 kg of water at 25°C. Find
the final
temperature or mixture. θ = 26.8oc
3. A iron ring of diameter 5.231 m is to be fixed on a wooden rim of diameter
5.243 m both initially
at 27°C. To what temperature should the iron
ring be heated so as to fit the rim (Coefficient of
linear expansion of iron
is1.2 × 105 k–1? 218oC
4. 100g of ice at 0°C is mixed with 100 g of water at 80°C. The resulting
temperature is 6°C. Calculate .heat of fusion
of ice. 68 cal/g.
5. Calculate heat required to convert 3kg of water at 0°C to steam at 100°C Given
specific heat capacity of H20 = 4186J
kg–1 k–1 and latent heat of steam = 2.256 × 106 J/kg
Total heat = 8023800J
6. A body re-emits all the radiation it receives. Find surface temperature of
the body. Energy received per unit area per unit time is 2.835 watt/m2
and α = 5.67 × 10–8 W m–2 k–4 85 k.
7. A thermodynamic system is taken from an original state to an intermediate state
by the linear
process
shown in Fig.Its volume is then reduced to the original value from E to F by an
isobaric
process.
Calculate the total work done by the gas from D to E to F.
450 J
8. What is the coefficient of performance (β) of a carnot
refrigerator working between 30°C and 0oC?
9.1
9. Calculate the fall in temperature when a gas initially at 72°C is expanded
suddenly to eight times its originalvolume.
(γ = 5/3) 86.25 k
10. Refrigerator is to maintain eatables kept inside at 9oC. If
room temperature is 36°C calculate the
coefficient
of performance.
10.4
11. A perfect carnot engine utilizes an ideal gas the source temperature is 500K
and sin temperature
is
375K. If the engine takes 600k cal percycle from the source, calculate
(i)
The efficiency of engine
25%
(ii)
Work done per cycle
450 k cal
(iii)
Heat rejected to sink per cycle.
450 k cal
12. Ten mole of hydrogen at NTP is compressed adiabatically so that its temperature
become 400oC
How
much work is done on the gas? What is the increase in the internal energy of
the gas R =
8.4
J mol–1 K–1 γ = 1.4 8.4×104 J
13. An air bubble of volume 1.0 cm3 rises from the bottom of a lake
40 m deep at a temperature of
12°C.
To what volume does it grow when itreaches the surface which is at a
temperature of
35oC?
5.3×10–6m3
14. A vessel is filled with a gas at a pressure of 76 cm of mercury at a
certain temperature. The
mass
of the gas is increased by 50% by introducing more gas in the vessel at the
same
temperature.
Find out the resultant pressure of the
gas. 114 cm of Hg.
15. One mole of a monoatomic gas is mixed with three moles of a diatomic gas.
What is the
molecular specific
heat of the mixture at constant volume? Take R = 8.31/mol–1 K–1.
18.7 J
mole–1 K–1
16. An oxygen cylinder of volume 30 litre has an initial gauge pressure of 15 atmosphere
and a
temperature
of 27°C. After some oxygen is withdrawn from the cylinder, the gauge pressure
drops
to 11 atmosphere and its temperature drop to 17°C. Estimate the mass of oxygen
taken out of
thecylinder(R = 8.31/mol–1 k–1) 0.140 kg. (molecular
mass of O2 = 32)
17. 0.014 kg of nitrogen is enclosed in a vessel at a temperature of 27°C. How
much heat has to be
transferred
to the gas to double the rms speed of its molecules. 2250 cal.
OSCILLATION AND WAVES
18. Find the period of vibrating particle (SHM), which has acceleration of
45cm s–2, when
displacement
from mean position is 5 cm 2.095 s
19. A 40 gm mass produces on extension of 4 cm in a vertical spring. A mass of
200 gm is suspended at its bottom and
left pulling down. Calculate the frequency of its vibration. 1.113 s–1
20. The acceleration due to gravity on the surface of the moon is 1.7 ms–2.What
is the time period of a simple pendulum
on the moon, if its time period on the earth is 3.5 s? [g = 9.8 ms–2]
8.4s
21. A particle executes simple harmonic motion of amplitude A.(i) At what
distance from the mean position is its kinetic
energy equal to its potential energy? (ii) At what points is its speed half the
maximum speed?
22. A particle executes S.H.M of amplitude 25 cm and time period 3s. What is
the minimum time
required
for the particle to move between two points 12.5 cm on either side of the mean
position?
0.5
s
23. The vertical motion of a huge piston in a machine is approximately S.H.M with
a frequency of 0.5 s–1. A
block of
10kg is placed on the piston. What is the maximum amplitude of the
piston’s S.H.M. for the block and piston
to remain together? 0.993m
24. At what temperature will the speed of sound be double its value at 273°K? 1092°K
25. A spring balance has a scale that reads from 0 to 50 kg. The length of the
scale is 20 cm. A body
suspended
from this spring, when displaced and released, oscillates with a period of 0.60
s. What
is
the weight of the body? 218.93 N.
26. If the pitch of the sound of a source appears to drop by 10% to a moving person,
then determine
the
velocity of motion of the person. Velocity of sound = 330 ms–1. 200
ms-1
27. A string of mass 2.5 kg is under a tension of 200N. The length of the stretched
string is 20m. If a transverse
jerk is struck at one end of the string, how long does the disturbance take to
reach the
other
end? 0.5 s
28. The equation of a plane progressive wave is given by the equation y = 10
sin 2π(t – 0.005x) where y and x are in cm and t in seconds.Calculate the
amplitude, frequency, wave length and velocity of the wave. 10 cm, 200
cm, 200 ms–1, 1 HZ
29. The length of a wire between the two ends of a sonometer is 105 cm. Where
should the two bridges be placed so that the fundamental frequencies of the
three segments are in the ratio of 1 : 3 : 15 ? Hence the bridges should be
placed at 75 cm and (75 + 25 =) 100 cm from one end.
30. A wire stretched between two rigid supports vibrates in its fundamental mode
with a frequency 45 Hz. The mass of the wire is 3.5×10–2 kg andits
linear density is 4.0×10–2 kg m–1 What is (a) the speed
of transverse wave on the string and (b) the tension in the string? 78.75 ms–1
31. A steel rod 100 cm long is clamped at its middle. The fundamental frequency
of longitudinal
vibrations
of the rod as given to be 2.53 kHz.What is the speed of sound in steel? 5.06
× 103 ms–1
