10 kW drilling machine is used to drill a bore in a small...

$\triangle 10 \mathrm{~kW}$ drilling machine is used to drill a bore in a small aluminium block of mass $8.0 \mathrm{~kg}$. 1low much is the rise in temperature of the block in $2.5$ minute? $\Lambda$ ssuming $50 \%$ of power is used up in heating the machine itself or lost the surroundings specific heat of aluminium $=0.91 \mathrm{~J} / \mathrm{g}-{ }^{\circ} \mathrm{C}$

Key Concepts

Heat Energy Equation

The heat energy equation, Q = m*c*?T, connects the energy absorbed (Q) with the mass (m) of the substance, its specific heat capacity (c), and the change in temperature (?T). This formula is fundamental in thermodynamics and calorimetry, providing the means to calculate the temperature increase resulting from a known energy input.

Specific Heat Capacity

Specific heat capacity is the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius. For the aluminum block, knowing its specific heat capacity allows us to relate the absorbed energy to the resulting temperature change, highlighting the intrinsic thermal properties of the material.

Power

Power is the rate at which energy is transferred or converted. In this context, it represents how much energy per unit time (measured in kilowatts) the drilling machine consumes, which is later used to heat up the aluminum block after accounting for efficiency losses. This concept is essential for determining the total energy input over the given operational time.

Energy Conversion Efficiency

Energy conversion efficiency refers to the fraction of the energy supplied that is effectively used for a particular purpose—in this case, heating the aluminum block. Since only 50% of the machine’s power contributes to heating the block while the rest is lost, understanding and applying efficiency is crucial for accurately calculating the net energy absorbed by the block.

Transcript

Please give Ace some feedback