Help visualizing this problem O.o Heat Prob

  • Thread starter Seiya
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In summary, to determine the minimum volume of the reservoir tank required for a hot-water heating system, you can use the volume equation with the radius and length of the pipe.
  • #1
Seiya
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Many hot-water heating systems have a reservoir tank connected directly to the pipeline, so as to allow for expansion when the water becomes hot. The heating system of a house has 52.1 m of copper pipe whose inside radius is 9.15 x 10- 3 m. When the water and pipe are heated from 24.9 to 65.4 °C, what must be the minimum volume of the reservoir tank to hold the overflow of water?

My prob: I know the 52.1m of copper pipe and the radius should give me a volume somehow so then i can solve the problem but i got no idea what this looks like :(


Doing this on stupid egrade thing from wiley... i already messed up one problem for hurrying (got the right answer after submitting the incorrect one :( ) so i can't mess this one up... any help would be greatly appreciated!
 
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  • #2
Answer: The minimum volume of the reservoir tank required to hold the overflow of water can be calculated using the equation for the volume of a cylinder, V = πr2h, where r is the radius of the pipe and h is the length of the pipe. With r = 9.15 x 10-3 m and h = 52.1 m, the minimum volume of the reservoir tank is 8.42 x 10-3 m3.
 
  • #3


First, let's visualize the problem by breaking it down into smaller parts. The hot-water heating system in the house has a reservoir tank connected directly to the pipeline. This means that the tank is connected to the pipe and acts as a storage unit for the hot water. The purpose of the tank is to allow for expansion of the water as it becomes hot, preventing any damage to the pipeline.

Next, we are given the length of the copper pipe (52.1m) and its inside radius (9.15 x 10^-3m). This information allows us to calculate the volume of the pipe using the formula V = πr^2h, where r is the radius and h is the length. This volume represents the maximum amount of water that can be held in the pipe without any expansion.

Now, we need to find the minimum volume of the reservoir tank to hold the overflow of water when the temperature of the water and pipe increases from 24.9 to 65.4 °C. This means that the water will expand and the excess water will flow into the reservoir tank. To calculate the volume of the overflow, we can use the formula V = m x ΔT x β, where m is the mass of the water, ΔT is the change in temperature, and β is the volumetric thermal expansion coefficient of water.

Finally, we can combine the two volumes (maximum volume of the pipe and overflow volume) to determine the minimum volume of the reservoir tank needed. This can be done by adding the two volumes together. The resulting volume will be the minimum volume of the reservoir tank required to hold the overflow of water when the temperature increases from 24.9 to 65.4 °C.

I hope this helps in visualizing the problem and approaching it step by step. Remember to always double check your calculations and take your time to avoid making mistakes. Best of luck with your egrade!
 

1. Can you explain the heat equation and how it applies to this problem?

The heat equation is a mathematical formula that describes how heat is transferred in a given system. It takes into account factors such as temperature, time, and heat conductivity to determine the rate of heat transfer. In this problem, the heat equation can be used to determine the temperature distribution over time in a specific object or system.

2. How can I visualize the heat transfer in this problem?

One way to visualize the heat transfer in this problem is to create a heat map, which uses colors to represent different temperatures in a given system. This can help to better understand the temperature distribution over time and identify any patterns or trends.

3. How does the initial temperature affect the heat transfer in this problem?

The initial temperature of a system can greatly impact the heat transfer. If the initial temperature is higher, it will take longer for the system to cool down as heat is transferred out. On the other hand, if the initial temperature is lower, the system will cool down more quickly as heat is transferred out.

4. Can you provide an example of a similar heat transfer problem?

One example of a similar heat transfer problem is a metal bar being heated at one end while the other end is kept at a constant temperature. The heat will transfer through the bar, causing the temperature to increase along its length. This problem can be solved using the heat equation.

5. Are there any limitations to using the heat equation to solve this problem?

While the heat equation is a useful tool for solving heat transfer problems, it does have some limitations. It assumes that the system is in a steady state and that the material being heated has constant properties. It also does not take into account any external factors that may affect the heat transfer, such as wind or humidity.

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