Thermal Properties of Matter

The temperature of a metal strip having coefficient of linear expansion is increased from T1 to T2 resulting in increase of its length by L1. The temperature is further increased from T2 to T3 such that the increase in its length is L2. Given T3+T1=2T2 and T2-T1= T, the value of L2 is .

1. L1 [1+2 2( T)2 ]
2. L1 [1+ 2( T)2 ]
3. L1 [1+2 T ]
4. L1 [1+ T ]

Which of the following best represents the temperature versus heat supplied graph for water, in the range of -20 C to 120 C?

1. [figure]
2. [figure]
3. [figure]
4. [figure]

10 kg of ice at -10 C is added to 100 kg of water to lower its temperature from 25 C. Consider no heat exchange to surroundings. The decrement to the temperature of water is C. (specific heat of ice = 2100 J/kg C, specific heat of water = 4200 J/kg C, latent heat of fusion of ice = 3.36 105 J/kg)

1. 15
2. 10
3. 6.67
4. 11.6

A brass wire of length 2 m and radius 1 mm at 27 C is held taut between two rigid supports. Initially it was cooled to a temperature of -43 C creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4T, is C.

1. -71
2. -80
3. -65
4. -86

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

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