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.

Asked by Abhisek | 1 year ago |  79

##### Solution :-

Power = 10 kW

Mass of the small aluminium block, m = 8 kg

= 8 x 103 g

Time = 2.5×60=150 s

Specific heat of aluminium, c= 0.91 J g–1 K–1.

Total energy =P×t=104 ×150=15×105 J

As 50% of the energy is used in the heating or lost to the surrounding,

Therefore, thermal energy available,

ΔQ= ($$\dfrac{1}{2}$$) x 15×105

= 7.5 x 105

As ΔQ=mcΔT

ΔT=$$\dfrac{ ΔQ}{mc}$$

=  $$\dfrac{7.5 \times 10^5}{(8 \times 10^3 ×0.91)}$$

$$\dfrac{7.5 \times 10^5}{7.28 \times 10^3}$$

= 1.03 x 10

Rise in the temperature of the block, ΔT = 103°C

Answered by Pragya Singh | 1 year ago

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