Thermal Properties of Matter · Question 48

The temperature of a metallic sphere of radius R is increased by a small amount T. If the linear coefficient of thermal expansion of the metal is , the approximate increase in the volume of the sphere is:

1. 6 R3 T
2. 2 R3 T
3. 3 R3 T
4. 4 R3 T

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2K while that in the middle has thermal conductivity K. The left end of the combination is maintained at temperature 3T and the right end at T. The rods are thermally insulated from outside. In steady state, temperature at the left junction is T1 and that at the right junction is T2. The ratio T1/T2 is [figure]

1. 53
2. 54
3. 32
4. 43

A metallic bar of Young's modulus, 0.5 1011 N m-2 and coefficient of linear thermal expansion 10-5 -1, length 1 m and area of cross-section 10-3 m2 is heated from 0 to 100 without expansion or bending. The compressive force developed in it is :

1. 5 103 N
2. 50 103 N
3. 100 103 N
4. 2 103 N

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the correct answer from the options given below.

1. A is true but R is false.
2. A is false but R is true.
3. Both A and R are true and R is the correct explanation of A.
4. Both A and R are true but R is NOT the correct explanation of A.

Two rods one made of copper and other made of steel of same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are 385 J s-1 K-1 m-1 and 50 J s-1 K-1 m-1 respectively. The free ends of copper and steel are held at 100 and 0 respectively. The temperature at the junction is, nearly :

1. 88.5
2. 12
3. 50
4. 73

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

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

The quantities of heat required to raise the temperature of two solid copper spheres of radii r1 and r2 (r1 = 1.5r2) through 1 K are in the ratio :

1. 94
2. 32
3. 53
4. 278

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is : ( Cu = 1.7 10-5 K-1 and Al = 2.2 10-5 K-1)

1. 119.9 cm
2. 88 cm
3. 68 cm
4. 6.8 cm

The unit of thermal conductivity is :

1. J m-1 K-1
2. W m K-1
3. J m K-1
4. W m-1 K-1

The power radiated by a black body is P and it radiates maximum energy at wavelength, 0. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength 34 0, the power radiated by it becomes nP. The value of n is

1. 34
2. 43
3. 25681
4. 81256