The specific heat of water is $4.18 J /( g \cdot{ }^{\circ} C )$ and that of wood is $1.97 J /( g \cdot{ }^{\circ} C )$. Which statement is correct?
A. Regardless of mass, wood will heat up less than water if the same heat is added.
B. Given equal masses, wood will heat up less than water if the same heat is added.
C. Given equal masses, water will heat up less than wood if the same heat is added.
D. Regardless of mass, water will heat up less than wood if the same heat is added.
Answer (1)
The heat formula is Q = m c Δ T , where Q is heat, m is mass, c is specific heat, and Δ T is the change in temperature.
Solving for Δ T , we get Δ T = m c Q .
With equal masses, since water has a higher specific heat, it will heat up less than wood.
Therefore, the correct statement is: Given equal masses, water will heat up less than wood if the same heat is added. $\boxed{Given equal masses, water will heat up less than wood if the same heat is added.}
Explanation
Problem Analysis We are given the specific heat of water, c w a t er = 4.18 J / ( g o b re ak s p a ce 0.166667 e m c d o t ∘ C ) , and the specific heat of wood, c w oo d = 1.97 J / ( g o b re ak s p a ce 0.166667 e m c d o t ∘ C ) . We want to determine which statement is correct regarding how water and wood heat up when the same amount of heat is added.
Heat Formula The formula relating heat, mass, specific heat, and temperature change is: Q = m c Δ T where:
Q is the heat added (in Joules),
m is the mass (in grams),
c is the specific heat (in J / ( g o b re ak s p a ce 0.166667 e m c d o t ∘ C ) ),
Δ T is the change in temperature (in ∘ C ).
Solving for Temperature Change We can rearrange the formula to solve for the change in temperature, Δ T :
Δ T = m c Q
Equal Mass Comparison Let's consider the case where the masses of water and wood are equal, i.e., m w a t er = m w oo d = m . Then, the change in temperature for water and wood are: Δ T w a t er = m c w a t er Q Δ T w oo d = m c w oo d Q Since c w a t er = 4.18 J / ( g o b re ak s p a ce 0.166667 e m c d o t ∘ C ) and c w oo d = 1.97 J / ( g o b re ak s p a ce 0.166667 e m c d o t ∘ C ) , we have c_{wood}"> c w a t er > c w oo d . Therefore, for the same mass m and heat Q ,
Δ T w a t er < Δ T w oo d This means that with equal masses, wood will heat up more than water when the same heat is added.
Statement Analysis Now, let's analyze the given statements:
Regardless of mass, wood will heat up less than water if the same heat is added. - This is incorrect because we showed that with equal masses, wood heats up more than water.
Given equal masses, wood will heat up less than water if the same heat is added. - This is incorrect, as we showed wood heats up more than water with equal masses.
Given equal masses, water will heat up less than wood if the same heat is added. - This is correct, as we showed Δ T w a t er < Δ T w oo d with equal masses.
Regardless of mass, water will heat up less than wood if the same heat is added. - This is incorrect. The temperature change also depends on the mass.
Conclusion Therefore, the correct statement is: Given equal masses, water will heat up less than wood if the same heat is added.
Examples
Imagine you have a wooden spoon and a metal spoon, both with the same mass, sitting in a pot of hot soup. Because wood has a lower specific heat than metal, the wooden spoon will heat up faster and become more comfortable to hold than the metal spoon. This principle is used in cooking and material selection to manage heat transfer effectively. Understanding specific heat helps us choose materials that either quickly absorb heat (like in cookware) or resist temperature changes (like in insulation).
