Question

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 $=0.90J{g}^{-10}{}^{-1})$

• A. $100$
• B. $103$
• C. $150$
• D. $155$

Answer 1

Answer: (B)

$103$

Here, $P=10kW={10}^{4}W,m=8kg$

time, $t=2.5minute=2.5\times 60=150s$

Specific heat, $s=0.91J{g}^{-1}{C}^{-1}$

Total energy $=P\times t={10}^4\times 150=15\times {10}^{5}J$

As 50% of energy is lost,

$\therefore$ Energy available, $\Delta Q=\frac{1}{2}\times 15\times {10}^5=7.5\times {10}^{5}J$

As $\Delta Q=ms\Delta T$

$\Delta T=\frac{\Delta Q}{ms}=\frac{7.5\times {10}^5}{8\times {10}^3\times 0.91}\approx 103$