Question

A 25 kW drilling machine is drilled for 4 minutes to bore a hole in an aluminium block of mass \(20 \times 10^3\) kg. If 40\% of the work done is utilized to raise the temperature of the block and if the specific heat of aluminium is \(0.9 \, {kJ/kg}^\circ C\), then the rise in temperature of aluminium block is:

• A. 266.3°C
• B. 66.66°C
• C. 133.3°C
• D. 70°C

Hint:

To calculate the temperature increase, use the formula \( Q = m \cdot c \cdot \Delta T \) and remember to factor in the percentage of work used for heating.

Answer 1

The Correct Option is C

The total work done by the machine is:

\[ \text{Work done} = P \times t = 25000 \, \text{J/s} \times 240 \, \text{s} = 6 \times 10^6 \, \text{J} \] 40% of this work is used to increase the temperature of the block:

\[ \text{Heat energy used} = 0.4 \times 6 \times 10^6 \, \text{J} = 2.4 \times 10^6 \, \text{J} \] The formula for heat energy is:

\[ Q = m \times c \times \Delta T \] Substituting the given values:

\[ 2.4 \times 10^6 = 20 \times 10^3 \times 900 \times \Delta T \] Solving for \( \Delta T \):

\[ \Delta T = \frac{2.4 \times 10^6}{20 \times 10^3 \times 900} = 133.3^\circ C \] Final Answer:
The rise in temperature is:
\[ \boxed{133.3^\circ C} \]