Question

A 10kW drilling machine is used to drill a bore in a small aluminum block of mass 8kg. Find the rise in temperature of the block in 2.5 minutes assuming $50\%$ power is used in heating the machine itself or lost to the surroundings.

A.)${100^0}C$
B.)${103^0}C$
C.)${105^0}C$
D.)${155^0}C$

Answer 1

Hint- In this question we will have to use the conservation of energy ,as it's given that $50\%$ of the amount of energy produced by the machine will be equal to the heat generated in the aluminum block thus we will calculate the temperature raised by applying formula .

Complete step-by-step answer:
Specific heat - It is the amount of heat used to raise the temperature of 1gram of material by ${1^0}$ Celsius.

Given

Power of the machine P = 10kW
Time for which the machine is being used
T = 2.5min
Mass of the aluminum block m = 8kg

The specific heat of the aluminum

$c = 0.91J/{g^0}C$

Also it is given that the $50\%$ of the energy used in heating the machine is lost in the surrounding

Therefore

$Q = 0.5Pt$

Let $\Delta T$ be the rise in the temperature of the block

As we know that $\left[ {Q = mc\Delta T} \right]$

$Q = mc\Delta T$

Substituting the values of m, c, Q from the given data, we get

$\Delta T = \dfrac{{7.5 \times {{10}^5}}}{{8 \times {{10}^3} \times 0.91}} = {103^0}C$

Hence the correct option is B.

Note- Aluminum heats up very fast this is because metals like aluminum are very good conductors of heat, so they absorb heat very quickly. The same property of being a good heat conductor ensures the foil cools down very quickly when you pull out the potato.