Question

A drilling machine of 10kW power is used to drill a bore in a small aluminium block of mass 8kg. If 50% of power is used up in heating the machine itself of lost to the surroundings then how much is the rise in temperature of the block in 2.5 min(given: specific heat of aluminium=0.91 $J/g^{\circ }C$)?

• A. 103°C
• B. 130°C
• C. 105°C
• D. 30°C

Answer 1

The correct option is (A) 103°C

Step 1, Given data

Power of machine = 10 kW

Mass (m) = 8 kg = 8000 g

Time (t) = 2.5 min = 150 sec

Specific heat capacity of the aluminum = 0.91J/$g^{0}C$

Step 2, Finding heat

Given that only 50% power is utilized

So, Power = 5 kW = 5000 W

We know,

$Power=\frac{Energy}{Time}$

Or,

$5000=\frac{Enerry}{150}$

$Or,Energy=750000J$

This energy is used to raise the temperature

Step 3, Finding a raise in temperature

We know,

$Q=mc\Delta t$

Where Q is heat energy. c is specific heat energy

Putting all the values

$750000=8000\times 0.91\times \Delta t$

$Or,\Delta t={103.02}^{0}C$

So, the rise in temperature is

${103.02}^{0}C$

Hence the correct option is (A)