An equal amount of heat is transferred to two containers containing water at the same temperature. If the
second container contains three times as many water molecules as the first, how do the final temperatures
compare?
To understand how the final temperatures compare, we need to consider the concept of specific heat capacity and the relationship between heat, temperature, and number of molecules.
The specific heat capacity of a substance measures how much heat energy is required to raise the temperature of a given mass of the substance by a certain amount. In this case, we are dealing with water, which has a specific heat capacity of approximately 4.18 J/g°C.
The heat transferred to a substance can be calculated using the formula:
Q = m * c * ΔT
Where:
Q is the heat transferred
m is the mass of the substance
c is the specific heat capacity of the substance
ΔT is the change in temperature
Now, let's analyze the situation:
1. The first container has a certain number of water molecules.
2. The second container has three times as many water molecules.
Since the mass of the water is directly proportional to the number of molecules, we can say:
m1 : m2 = n1 : n2
Where:
m1 and m2 are the masses of the water in the first and second containers, respectively.
n1 and n2 are the number of water molecules in the first and second containers, respectively.
Since the heat transferred is equal, we can set up the equation:
Q1 = Q2
Using the formula above, we can rewrite this equation as:
m1 * c * ΔT1 = m2 * c * ΔT2
Considering that m2 = 3 * m1 (because the second container contains three times as many water molecules as the first), we can substitute this into the equation:
m1 * c * ΔT1 = (3 * m1) * c * ΔT2
Dividing both sides of the equation by m1 * c, we get:
ΔT1 = 3 * ΔT2
This equation tells us that the change in temperature in the first container is three times the change in temperature in the second container.
In terms of the final temperatures, if the initial temperatures of both containers were the same, the final temperature in the first container would be three times the final temperature in the second container.
So, the final temperatures are not equal; the final temperature in the first container is three times the final temperature in the second container.