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Thermal Properties of Matter — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsThermal Properties of Matter5 Marks
Question
A $10kW$ drilling machine is used to drill a bore in a small aluminium block of mass $8.0kg$. 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 surroundings. Specific heat of aluminium = $0.91J g^{–1} K^{–1}$.
✓

Answer

Power of the drilling machine, $P = 10kW = 10 \times 10^3W$
Mass of the aluminum block, $m = 8.0kg = 8 \times 10^3g$
Time for which the machine is used, $t = 2.5min = 2.5 \times 60 = 150s$
Specific heat of aluminium, $c = 0.91J g^{–1} K^{–1}$
Rise in the temperature of the block after drilling = $\delta\text{T}$
Total energy of the drilling machine = Pt
$= 10 \times 10^3\times 150$
$= 1.5 \times 10^6J$
It is given that only 50% of the power is useful. Useful energy, $\triangle\text{Q}=\Big(\frac{50}{100}\Big)\times1.5\times10^6=7.5\times10^5\text{J}$
But $\triangle\text{Q}=\text{mc}\triangle\text{T}$
$\therefore\triangle\text{T}=\frac{\triangle\text{Q}}{\text{mc}}$
$=\frac{(7.5\times10^5)}{(8\times10^3\times0.91)}$
$=103^\circ\text{C}$
Therefore, in 2.5 minutes of drilling, the rise in the temperature of the block is 103°C.

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