Question

A 10 kW drilling machine is used to drill a bore in a small aluminum 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 aluminum $0.91J/g$ )
A. 100
B. 103
C. 150
D. 155

Answer 1

Hint: We have a drilling machine used to drill a bore and the power of the machine is given. We are asked to find the increase in temperature in 2.5 minutes. We know the relation between heat energy, power and time. Using that we can find the net heat energy. Since 50% of this energy is used for heating the machine, 50% of the net energy can be reduced. By the equation for energy required to raise the temperature, we get the rise in temperature.
Formula used:
Energy,
$E=P\times t$
Energy required for raising the temperature,
$\Delta E=mST$

Complete answer:
The power of the machine used to drill the bore is given to us.
Power, P = 10 KW$={{10}^{4}}J{{s}^{-1}}$.
The mass of the aluminum block is also given, m= 8 Kg.
We assume that 50% of the power of the machine is used to heat the machine; we have to find the rise in temperature of the block in 2.5 minutes.
Time, t =2.5 min = 150 seconds.
The equation for the produced heat energy is given as,
$E=P\times t$, were ‘E’ is the energy produced, ‘P’ is the power and ‘t’ is the time.
By substituting the values of power and time in the equation, the total energy,

 $\begin{align}
  & E={{10}^{4}}\times 150 \\
 & E=1.5\times {{10}^{6}}J \\
\end{align}$

It is said that 50% of the total energy delivered is used by the machine to heat itself.
Therefore the remaining amount of energy,
$\Delta E=\dfrac{\left( 1.5\times {{10}^{6}} \right)}{100}\times 50$
$\Delta E=7.5\times {{10}^{5}}J$

We know that the energy required to raise the temperature is given by
$\Delta E=mST$ , were ‘m’ is mass, ‘S’ is the specific heat and ‘T’ is rise in temperature.
We have to find the temperature, ‘T’

$T=\dfrac{\Delta E}{m{{h}_{s}}}$

By substituting the known values, we get

$\begin{align}
  & T=\dfrac{7.5\times {{10}^{5}}}{8\times {{10}^{3}}\times 0.91} \\
 & T=103.02\approx {{103}^{o}}C \\
\end{align}$

Therefore, the rise in temperature of the block in 2.5 minutes$={{103}^{0}}C$

So, the correct answer is “Option B”.

Note:
Calorimetry helps us to find out the final temperature of a body, by analyzing heat exchange when two or more than two bodies with different temperatures are mixed together.

We know that, when two such bodies are mixed together, heat flows from the body with higher temperature to the body with lower temperature. This process continues until both bodies have the same temperature.

According to the principle of Calorimetry, the heat gained by a body is equivalent to the heat lost by the other body.