I'm trying to rank the maximum temperatures of water at 20 degrees Celsius after adding in heated copper cylinders. The first case is 1 cylinder at 22.5 degrees Celsius. Second is two cylinders at 25 degrees Celsius. Third is 3 cylinders at 25 degrees Celsius. Lastly, 1 cylinder at 15 degrees Celsius. This is the Think and Rank #21 from Chapter 21 of Paul Hewitt's Conceptual Physics book. I'm confused on what I need to solve this, like specific heat capacity or what.
Three cylinders at 25 C will add more heat to the water than two at the same temperature.
Two cylinders at 25 C will add more heat to the water than one cylinder at 22.5 C.
Finally, the 1 cylinder at 15 C will cool the water.
(Remember that the water starts out at 20 C)
That brief bit of logic should make the ranking easy. You don't have to do the numbers. That is why they call it a conceptual physics clAss.
To solve this problem and rank the maximum temperatures of water, you will need to use the concept of specific heat capacity. Specific heat capacity is a measure of how much heat energy is required to raise the temperature of a substance by a certain amount.
In this case, you are adding heated copper cylinders to the water, so you need to consider the transfer of heat energy from the cylinders to the water. The equation you can use to calculate the heat transfer is:
Q = mcΔT
where Q is the heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
In this problem, the mass of the water and the specific heat capacity of water are constant. You are comparing different scenarios with varying temperature changes and different numbers of copper cylinders. The maximum temperature reached by the water will depend on the amount of heat transferred to it.
Let's break down each scenario:
1. In the first case, you have 1 cylinder at 22.5 degrees Celsius. To calculate the heat transferred to the water, subtract the initial temperature (20 degrees Celsius) from the cylinder temperature (22.5 degrees Celsius). Then use the equation Q = mcΔT.
2. In the second case, you have two cylinders at 25 degrees Celsius. Similarly, calculate the heat transferred by subtracting the initial temperature (20 degrees Celsius) from the cylinder temperature (25 degrees Celsius). Then use the equation Q = mcΔT.
3. In the third case, you have three cylinders at 25 degrees Celsius. Again, calculate the heat transferred by subtracting the initial temperature (20 degrees Celsius) from the cylinder temperature (25 degrees Celsius). Use the equation Q = mcΔT.
4. In the fourth case, you have 1 cylinder at 15 degrees Celsius. Calculate the heat transferred by subtracting the initial temperature (20 degrees Celsius) from the cylinder temperature (15 degrees Celsius). Use the equation Q = mcΔT.
By comparing the values of heat transferred in each case, you can rank the maximum temperatures reached by the water. The higher the heat transferred, the higher the maximum temperature will be.