__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

^{–7}m 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 = 26.8**

^{o}c**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 × 10

^{5}k^{–1}?**218**^{o}C**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 × 10

^{6 }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/m

^{2}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 0

^{o}C?

**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 9

^{o}C. 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 400

^{o}C

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

**8.4×10**^{4 }J**13.**An air bubble of volume 1.0 cm

^{3}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

35

^{o}C?**5.3×10**^{–6}m^{3}**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 × 10**^{3}ms^{–1}