Thermal Properties of Matter NCERT Solutions Class 11 Physics - Solved Exercise Question 11.12

Question 11.12:
A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the machine itself or lost to the surroundings. Specific heat of aluminium = 0.91 J g–1 K–1.
Solution:
Power of the drilling machine, P = 10 kW = 10 × 103 W
Mass of the aluminum block, m = 8.0 kg = 8 × 103 g
Time for which the machine is used, t = 2.5 min = 2.5 × 60 = 150 s
Specific heat of aluminium, c = 0.91 J g–1 K–1
Rise in the temperature of the block after drilling = δT
Total energy of the drilling machine = Pt
= 10 × 103 × 150
= 1.5 × 106 J
It is given that only 50% of the power is useful.
Useful energy, ∆Q = (50/100) X 1.5 X 106  =  7.5 X 105 J
But ∆Q = mc∆T
∆T = ∆Q / mc
= (7.5 X 105) / (8 X 103 X 0.91)
= 103o C
Therefore, in 2.5 minutes of drilling, the rise in the temperature of the block is 103°C.

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