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How much heat energy is required to raise the temperature of 0.368kg of copper from 23.0 ∘C to 60.0 ∘C? The specific heat of copper is 0.0920 cal/(g⋅∘C)

Verified Answer :

The change in temperature here corresponds to a sensible heat. The amount of energy required can be calculated by multiplying the specific heat capacity, the amount of the substance and the corresponding change in temperature.

Heat required = mCΔT
Heat required = 0.368 kg (0.0920 cal/g°C) (60 - 23)°C
Heat required = 1.25 cal

The heat required to raise the temperature of the copper is \(\boxed{1252.6\,{\text{cal}}}\).


Further Explanation:

Given:


The mass of the copper is \(0.368\,{\text{kg}}\).

The specific heat capacity of copper is \(0.0920\,\text{cal/g}\cdot^\circ\text{C}\) .


Concept:


The specific heat capacity of a particular substance is the amount of energy required to raise the temperature of unit mass of the substance by \(1\,^\circ {\text{C}}\).


The change I temperature required to heat the copper is given as.

\(\Delta T = {T_f} - {T_i}\)  


Substitute the final and initial values of temperature.

\(\begin{aligned}\Delta T &= 60 - 23\,^\circ {\text{C}} \\&= {\text{37}}\,^\circ {\text{C}} \\\end{aligned}\)  


The expression for the amount of heat required to raise the temperature of the copper is.

 \(\boxed{Q = mC\Delta T}\)


Here, \(Q\) is the amount of heat required, \(m\) is the mass of the substance, \(C\) is the specific heat capacity and \(\Delta T\) is the change in temperature required.


Substitute the values in above expression.

\(\begin{aligned}Q&=368\,\text{g}\times(0.0920\,\text{cal/g}\cdot{^\circ\text{C}})\times(37\,{^\circ}\text{C})\\&=1252.6\,\text{cal}\end{aligned}\)  


Thus, the amount of heat required to raise the temperature of the copper from \(23\,{\text{^\circ C}}\) to \(60\,{\text{^\circ C}}\) is \(\boxed{1252.6\,{\text{cal}}}\).


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Answer Details:

Grade: High School

Chapter: Heat transfer

Subject: Physics


Keywords:  Heat energy, raise the temperature, substance, copper, unit mass, heat required, specific heat, mass, 23 C to 60 C, capacity.