Thermal Properties of Matter

The heat extracted out of x gram of water initially at 50 °C to cool it down to 0 °C is sufficient to evaporate (1000-x) gram of water also initially at 50 °C. The value of x (closest integer) is . (Take latent heat of water 2256 kJ/kg, specific heat capacity of water 4200 J/kg. K)

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

A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50 . The gas is now heated to double its temperature. The modified pressure is Pa.

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)

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have

1. low thermal conductivity and high electrical conductivity
2. low thermal conductivity and low electrical conductivity
3. high thermal conductivity and high electrical conductivity
4. high thermal conductivity and low electrical conductivity

A cup of coffee cools from 90 to 80 in t minutes when the room temperature is 20 . The time taken by the similar cup of coffee to cool from 80 to 60 at the same room temperature is:

1. 135t
2. 1013t
3. 513t
4. 1310t

The temperature of a body in air falls from 40 to 24 in 4 minutes. The temperature of the air is 16 . The temperature of the body in the next 4 minutes will be :

1. 283
2. 563
3. 423
4. 143

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?

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

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J, then the mass of the bullet is grams. (Latent heat of fusion of lead =2.5 104 J Kg-1 and specific heat capacity of lead =125 J Kg-1 K-1)

1. 20
2. 15
3. 5
4. 10

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

1. 64 E
2. 16 E
3. E
4. 256 E

An amount of ice of mass 10-3 kg and temperature -10 C is transformed to vapour of temperature 110 C by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice =2100 J kg-1 K-1, specific heat of water =4180 J kg-1 K-1, specific heat of steam =1920 J kg-1 K-1, Latent heat of ice =3.35 105 J kg-1 and Latent heat of steam =2.25 106 J kg-1 )

1. 3022 J
2. 3043 J
3. 3003 J
4. 3024 J

Three conductors of same length having thermal conductivity k1,k2 and k3 are connected as shown in figure. [figure] Area of cross sections of 1st and 2nd conductor are same and for 3rd conductor it is double of the 1st conductor. The temperatures are given in the figure. In steady state condition, the value of is . (Given : k1=60 Js-1 m-1 K-1, k2=120 Js-1 m-1 K-1, k3=135 Js-1 m-1 K-1 )

On Celsius scale the temperature of body increases by 40 . The increase in temperature on Fahrenheit scale is :

1. 75
2. 70
3. 72
4. 68

A block of ice at -10 C is slowly heated and converted to steam at 100 C. Which of the following curves represent the phenomenon qualitatively:

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