Question

A $10kW$ drilling machine is used to drill a bore in a small aluminium block of mass $8kg$. 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$=0.91J{g}^{-1}{}^o{C}^{-1})$

• A. ${100}^{o}C$
• B. ${103}^{o}C$
• C. ${150}^{o}C$
• D. ${155}^{o}C$

Answer 1

Answer: (B)

${103}^{o}C$

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,$△Q=\frac{1}{2}\times 15\times {10}^5=7.5\times {10}^{5}J$

As$△Q=ms△T$
$△T=\frac{△Q}{ms}=\frac{7.5\times {10}^5}{8\times {10}^3\times 0.91}\approx {103}^{o}C$