Answer:
(A) - m=0.558 kg
(B) - Q=65.4 kJ
(C) - Compared with iron, water requires more heat to change its temperature because its specific heat is greater than that of iron.
Conceptual:
What is heat?
Heat is a form of energy and is associated to the motion of atoms and molecules.
What is meant by the specific heat of a substance?
The specific heat of a substance is a calculated value that is a ratio of the amount of heat required to raise the temperature by one unit of mass. When introduced to thermodynamics you will have a table in your physics textbook to look up the specific heat of a substance.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Formula to Calculate Heat: }}\\\\Q=mc\Delta T\end{array}\right }\\\\[/tex]
Where...
i. "m" is the mass of the substance
ii. "c" is the specific heat of the substance, which can be found in a table online or in a physics textbook
iii. "ΔT" is the change in temperature that the object undergoes
Explanation:
Given the three part question.
(A) - Given that 7000 J of heat is added to a piece of iron and that its change in temperature equals 28.0°C, find the piece if iron's mass.
(B) - How much heat would you have to add to an equal mass of water to get the same change in temperature?
(C) - Explain the difference in your results for Parts (A) and (B).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Part (A):
Given:
[tex]Q= 7000 \ J\\\\\Delta T= 28\textdegree C\\\\c_i=448 \ \frac{J}{kg \cdot \textdegree C}[/tex]
Find:
[tex]m_i=?? \ kg[/tex]
Plug the values we know into the formula for heat.
[tex]Q_i=m_ic_i\Delta T\\\\\Longrightarrow 7000=m_i(448)(28)\\\\\Longrightarrow 7000=12544m_i\\\\\therefore \boxed{\boxed{m_i=0.558 \ kg}}[/tex]
Thus, the mass of the piece of iron is found.
Part (B):
Given:
[tex]m_w= 0.558 \ kg\\\\\Delta T= 28\textdegree C\\\\c_w=4186 \ \frac{J}{kg \cdot \textdegree C}[/tex]
Find:
[tex]Q_w=?? \ J[/tex]
Plug the values we know into the formula for heat.
[tex]Q_w=m_wc_w\Delta T\\\\\Longrightarrow Q_w=(0.558)(4186)(28)\\\\ \Longrightarrow Q_w=65402.1 \ J\\\\\therefore \boxed{\boxed{Q_w=65.4 \ kJ}}[/tex]
Thus, the amount of heat required to heat the same mass of water is found.
Part (C):
Comparing our answers from Part (A) and Part (B) we notice that it takes significantly more heat to heat up an equal mass of water with the same change in temperature compared to the piece of iron. Why is that? To put it simply, it's because the specific heat of water is greater than that of iron's. It takes more heat to raise the temperature of 1 kg of water one degree Celsius.
