Question 1

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

Accepted Answer

The initial volume of the metallic sphere is V = 4 3 R^3. The coefficient of volume expansion is related to the linear coefficient of thermal expansion as = 3 . The increase in volume V due to a temperature increase T is given by V = V T. Substituting the values of V and , we get: V = ( 4 3 R^3 )(3 ) T V = 4 R^3 T Answer: 4 R^3 T

Question 2

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2 K while that in the middle has thermal conductivity K. The left e

Accepted Answer

aligned & In steady state ( dQ dt )_1= ( dQ dt )_2= ( dQ dt )_3 \ & 2 KA (3 ~T - T _1 ) L = KA ( ~T _1- T _2 ) L = 2 KA ( ~T _2- T ) L \ & 6 ~T -2 ~T _1= T _1- T _2=2 ~T _2-2 ~T \ & 6 ~T -2 ~T _1= T _1- T _2 \ & 6 ~T + T _2=3 ~T _1 ....(i)\ & ~T _1- T _2=2 ~T _2-2 ~T \ & 2 ~T -3 ~T _2=- T _1.....(ii) aligned Multiply equation (2) By ' 3 ' 6 ~T -9 ~T _2=-3 ~T _1....(iii) Equation (1) - (3) aligned & 10 ~T _2=6 ~T _1 \ & ~T _1 ~T _2 = 5 3 aligned

Thermal Properties of Matter — Previous Year Questions & Solutions