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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 kg. Find the rise in temperature of the block in `2.5` minutes, assuming `50%` power is used up in heating the machine itself or lost to the surroundings.
(Specific heat of aluminium `= 0.91 J g^(-1).^(@)C^(-1)`)

A

`100 .^(@)C`

B

`103 .^(@)C`

C

`150 .^(@)C`

D

`155 .^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `P = 10 kW = 10^(4) W, m = 8 kg`
time, `t = 2.5` minute `= 2.5 xx 60 = 150 s`
Specific heat, `s = 0.91 j g^(-1) C^(-1)`
Total energy `= P xx t = 10^(4) xx 150 = 15 xx 10^(5) J`
As `50%` of energy is lost,
`:.` Energy available, `DeltaQ = 1/2 xx 15 xx 10^(5) = 7.5 xx 10^(5) J`
As `DeltaQ = msDeltaT`
`DeltaT = (DeltaQ)/(ms) = (7.5 xx 10^(5))/(8 xx 10^(3) xx 0.91) ~~ 103 .^(@)C`
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