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`.

Explanation

Here `P = 10 kW =10^4 W, mass m = 8.0 kg = 8 xx10^3 g`
rise in temp. `Delta = ?, time , t = 2.5 min = 2.5 xx 60 = 150 s`
Sp. Heat, `s = 0.91 J g^(-1) .^@C^(-1)`
Total energy, ` = P xx t = 10^4xx150 = 15xx10^5 J`
As, 50 % of energy is lost, `:.` Energy available, `Delta Q = (1)/(2)xx15 xx 10^5 = 7.5 xx 10^5 J`
As `Delta Q =ms Delta T :. Delta T = (Delta Q)/(ms) = (7.5 xx10^5)/(8xx10^3 xx 0.91) = 103 .^@C`