Thermal Properties of Matter · Question 6

An air bubble of volume 2.9 cm3 rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17 . The volume of the bubble when it reaches the surface, where the water temperature is 27 , is cm3. (g = 10 m/s2, density of water = 103 kg/m3, and 1 atm pressure is 105 Pa)

1. 2.0
2. 4.2
3. 3.0
4. 4.5

Rods x and y of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points A and F are maintained at 100 and 40 respectively. Given the thermal conductivity of rod x is three times of that of rod y, the temperatures at junction points B and E are (close to): [figure]

1. 60 and 45 respectively
2. 80 and 70 respectively
3. 89 and 73 respectively
4. 80 and 60 respectively

An aluminium and a steel rod having same lengths and cross-sections are joined to make total length of 120 cm at 30 . The coefficients of linear expansion of aluminium and steel are 24 10-6/ and 1.2 10-5/ , respectively. The length of this composite rod when its temperature is raised to 100 , is cm.

1. 120.20
2. 120.06
3. 120.15
4. 120.03

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27 to 87 . The rate of consumption of the gas is g/s. (Take heat of combustion of gas = 5.0 104 J/g, specific heat capacity of water = 4200 J/kg C)

1. 4.2
2. 2.1
3. 0.21
4. 0.42

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take g = 10 m/s2, specific heat of water = 4200 J/(kg K))

1. 0.36 K
2. 0.23 K
3. 0.48 K
4. 0.14 K

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727 and power radiated by the wire is 94.2 W. Its emissivity is x8 where x = . (Given = 6.0 10-8 W m-2 K-4, = 3.14 and assume that the emissivity of wire material is same at all wavelengths.)

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal conductivities of these rods are: LALB = 12, rArB = 2 and KAKB = 12. The free ends of rods A and B are maintained at 400 K, 200 K, respectively. The temperature of rods interface is K, when equilibrium is established.

Consider a rectangular sheet of solid material of length l = 9 cm and width d = 4 cm. The coefficient of linear expansion is = 3.1 10-5 K-1 at room temperature and one atmospheric pressure. The mass of sheet m = 0.1 kg and the specific heat capacity Cv = 900 J kg-1 K-1. If the amount of heat supplied to the material is 8.1 102 J then change in area of the rectangular sheet is :

1. 2.0 10-6 m2
2. 6.0 10-7 m2
3. 3.0 10-7 m2
4. 4.0 10-7 m2

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4\% when heated by 1 . Its initial temperature must be:

1. 2500 K
2. 25
3. 250
4. 250 K

Match List - I with List - II. Choose the correct answer from the options given below :

1. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
2. (A)-(III), (B)-(I), (C)-(II), (D)-(IV)
3. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
4. (A)-(II), (B)-(III), (C)-(I), (D)-(IV)