Solving a Lightning Storm Homework Problem

In summary, the conversation discusses the calculation of the amount of sap that can be boiled away from a tree due to lightning strike. The solution involves calculating the energy absorbed by the tree, which is 1% of the total energy of 50.0 C of charge accelerated through a potential difference of 1.50 x 10^8 V. Using the specific heat and latent heat of vaporization of water, the amount of sap that can be vaporized is determined to be 29.19 kg. There may be discrepancies with the answer provided by WebAssign.
  • #1
vdeity
6
0

Homework Statement



A certain storm cloud has a potential of 1.50 x 10^8 V relative to a tree. If, during a lightning storm, 50.0 C of charge is transferred through this potential difference and 1.00% of the energy is absorbed by the tree, how much sap in the tree can be boiled away? Model the sap as water initially at 26.0°C. Water has a specific heat of 4186 J/(kg·C°), a boiling point of 100°C, and a latent heat of vaporization of 2.26 x 10^6 J/kg.


Homework Equations



I'm actually kinda iffy on all the equations, but I got several answers that WebAssign told me was wrong...

The Attempt at a Solution



Energy gain of 50.0 C of charge accelerated through potential difference of (1.50 x 10^8 V) is (50.0 C)(1.50 x 10^8 V) = 7.5 x 10^9 J.

To vaporize 1 kilogram of sap requires mcΔT = (1 kg)(4186 J/kg K)(100 - 26 degrees C) = 3.098 x 10^(5) J to heat to 100 degrees C

An additional 2.26 x 10^6 J for the state change from liquid to gas, for a total required energy of 3.098 x 10^(5) + 2.26 x 10^6 = 2.57 x 10^6 J.

The total energy absorbed is 1% of 7.5 x 10^9 = 7.5 x 10^7 J, and at 2.57 x 10^6 J per kg needed, we are able to vaporize:

(7.5 x 10^7 J)/(2.57 x 10^6 J/kg) = 29.19 kg of sap.

WebAssign says it's wrong.

Please tell me where I went wrong.
It isn't due for a few days, I just wanted to get this assignment out of the way... Last question.

Thanks!
 
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  • #2


WebAssign is evil. I see nothing wrong with your solution - your method is OK and I verified your numbers. It may be a matter of sig figs or (perish the thought) the wrong calculated formula has been put into the problem. I suggest that you take your solution to your instructor and ask him/her to find what is wrong with it. Do this before the deadline.
 
  • #3


Sorry to bring up an old thread, but I was under the impression that the energy absorbed by the tree will be equal to 1/2QV, and not QV. I'd be curious to hear what others have to say about this.

Thanks,

Tom
 
  • #4


That would be true if you had a capacitor with 50C on it that you let completely discharge.
The question doesn't say that the stormcloud completely discharges however.
 
  • #5


I see what you're saying. Thanks.
 

What is a Lightning Storm Homework Problem?

A Lightning Storm Homework Problem is a scientific question or puzzle related to understanding the nature and behavior of lightning storms. It may involve analyzing data, conducting experiments, or formulating hypotheses to explain observed phenomena.

Why is it important to solve a Lightning Storm Homework Problem?

Solving a Lightning Storm Homework Problem is important because it allows us to gain a better understanding of the natural world and the forces at work during a lightning storm. This knowledge can help us develop better safety measures and predict potential hazards.

What are some common approaches to solving a Lightning Storm Homework Problem?

Some common approaches to solving a Lightning Storm Homework Problem include conducting experiments in a controlled environment, analyzing data from previous lightning storms, and using mathematical models to simulate lightning behavior.

What are some challenges that may arise when solving a Lightning Storm Homework Problem?

One challenge that may arise when solving a Lightning Storm Homework Problem is the unpredictable and dangerous nature of lightning storms. It may also be difficult to gather accurate data or replicate lightning strikes in a controlled setting. Additionally, the complexity of the physics involved in lightning may present challenges in developing accurate models and theories.

How can solving a Lightning Storm Homework Problem contribute to scientific knowledge?

Solving a Lightning Storm Homework Problem can contribute to scientific knowledge by expanding our understanding of the mechanisms involved in lightning storms. It can also help us develop more accurate models and predictions, which can aid in the development of new technologies and safety measures. Additionally, solving a Lightning Storm Homework Problem may lead to new discoveries and advancements in the field of atmospheric science.

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