Question:
A hammer of mass $200\, kg$ strikes a steel block of mass $200\, g$ with a velocity $8\, ms^{-1}$. If $23\%$ of the energy is utilized to heat the steel block, the rise in temperature of the block is (specific heat capacity of steel = $460 \; J \; kg^{-1} \; K^{-1}$)
A hammer of mass $200\, kg$ strikes a steel block of mass $200\, g$ with a velocity $8\, ms^{-1}$. If $23\%$ of the energy is utilized to heat the steel block, the rise in temperature of the block is (specific heat capacity of steel = $460 \; J \; kg^{-1} \; K^{-1}$)
Updated On: Jan 18, 2023
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The Correct Option is B
Solution and Explanation
Given, mass of hammer, $m=200\, kg$,
steel block of the mass $=200 \,g =0.2 \,kg$
and specific heat capacity of steel, $s=460 \,J \,kg ^{-1} K ^{-1}$
Velocity of hammer, $v=8 \,ms ^{-1}$
As we know that, Kinetic energy, $KE =\frac{1}{2} m v^{2}$
Putting the given values, we get
$=\frac{1}{2} \times 200 \times 8^{2}=6400\, J$
Hence, the $23 \%$ of this energy is converted to heat.
$\Rightarrow H=\frac{6400 \times 23}{100}=1472\, J$
The rise in temperature of steel,
$\Delta T=\frac{H}{m s}=\frac{1472}{460 \times 0.2}=16\, K$
Hence, the rise in temperature is $16\, K$.
steel block of the mass $=200 \,g =0.2 \,kg$
and specific heat capacity of steel, $s=460 \,J \,kg ^{-1} K ^{-1}$
Velocity of hammer, $v=8 \,ms ^{-1}$
As we know that, Kinetic energy, $KE =\frac{1}{2} m v^{2}$
Putting the given values, we get
$=\frac{1}{2} \times 200 \times 8^{2}=6400\, J$
Hence, the $23 \%$ of this energy is converted to heat.
$\Rightarrow H=\frac{6400 \times 23}{100}=1472\, J$
The rise in temperature of steel,
$\Delta T=\frac{H}{m s}=\frac{1472}{460 \times 0.2}=16\, K$
Hence, the rise in temperature is $16\, K$.
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Concepts Used:
Specific Heat Capacity
Specific heat of a solid or liquid is the amount of heat that raises the temperature of a unit mass of the solid through 1°C.
Molar Specific Heat:
The Molar specific heat of a solid or liquid of a material is the heat that you provide to raise the temperature of one mole of solid or liquid through 1K or 1°C.
Specific Heat at Constant Pressure or Volume:
The volume of solid remains constant when heated through a small range of temperature. This is known as specific heat at a constant volume. It is denoted as CV.
The pressure of solid remains constant when heated through a small range of temperature. This is known as specific heat at constant pressure which can be denoted as CP.