Question

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​

Answer 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) × 1.5 × 106 = 7.5 × 105 J

But ∆Q = mc∆T

∴ ∆T = ∆Q / mc

= (7.5 × 105) / (8 × 103 × 0.91)

= 103o C

Therefore, in 2.5 minutes of drilling, the rise in the temperature of the block is 103°C.

Answer 2

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Refer the attachment.