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 $= 0.91\, J \,g^{-1} \,{}^{\circ}C^{-1}$)

• A. $100 \,{}^{\circ}C$
• B. $103 \,{}^{\circ}C$
• C. $150 \,{}^{\circ}C$
• D. $155 \,{}^{\circ}C$

Answer 1

Answer: (B)

Here, $P = 10\, kW = 10^4\, W$, $m = 8 \,kg$
time, $t = 2.5\, minute = 2.5 \times 60 = 150 \,s$
Specific heat, $s = 0.91\, J \,g^{-1}\, C^{-1}$
Total energy $= P \times t = 10^4 \times 150 = 15 \times 10^5 \,J$
As $50\%$ of energy is lost,
$\therefore $ Energy available, $\Delta Q=\frac{1}{2}\times15\times10^{5}=7.5 \times10^{5}\,J$
As $\Delta Q=ms\Delta T$
$\Delta T=\frac{\Delta Q}{ms}=\frac{7.5 \times 10^{5}}{8 \times 10^{3} \times 0.91}\approx103 \,{}^{\circ}C$