Thermal Properties of Matter · Question 14

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

Answer

(1) 2.0 10-6 m2

Solution

Rise in temperature of the sheet:

Q = mCv T

T = QmCv = 8.1 1020.1 900 = 9 K

Coefficient of area expansion: = 2 = 6.2 10-5 K-1

Initial area: A = l d = 9 4 = 36 cm2 = 36 10-4 m2

A = A T = 6.2 10-5 36 10-4 9

A 2.0 10-6 m2

Answer: (1)