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A 10 kW drilling machine is used to dril...

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 surrounding? Specific heat of aluminium `= 0.91 J//g^(@)C`.

A

`103^(@)`C

B

`130^(@)`C

C

`105^(@)`C

D

`30^(@)`C

Text Solution

Verified by Experts

`P= W/t`
Total work done by drill machine in `2.5 xx 60` s = `(10 xx 10^(3))(2.5 xx 60) = 15 xx 10^(5)`J
`therefore` Energy lost = 50% of 15 `xx10^(5)`J = `7.5 xx 10^(5)`J
Energy taken by its surroundings, I.e. aluminium block.
`DeltaQ= mcDeltat = 8 xx 10^(3) xx 0.91 x DeltaT`
`DeltaT = 103^(@)`C
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