What Are the Dimensions of kWh?

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Discussion Overview

The discussion revolves around the dimensional analysis of kilowatt-hours (kWh), exploring its representation in terms of fundamental dimensions. Participants are examining whether kWh can be expressed as M L² T⁻² or if it should be represented differently, considering its relationship to energy and time.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether the dimensions of kWh are M L² T⁻² and seeks clarification on the reasoning behind this.
  • Another participant explains that a watt is defined as a Newton-meter per second, leading to the expression of kWh in terms of force, distance, and time.
  • A later reply reiterates the explanation of kWh as a unit of energy, confirming that its dimensions align with those of energy, M L² T⁻².
  • There is a discussion about the mixed time units in kWh and whether it is useful to convert to base units, indicating some uncertainty about the implications of this conversion.

Areas of Agreement / Disagreement

Participants express differing views on the dimensional representation of kWh, with some agreeing on M L² T⁻² while others raise questions about the appropriateness of this representation due to the mixed time units involved.

Contextual Notes

There are unresolved aspects regarding the conversion of kWh to base units and the implications of mixed time units on dimensional analysis.

nineteen
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What are the dimensions of kilo Watt hours? Is is M L2T-2?? If yes, why is that? If no, please teach me about what the right dimensions are and please be kind enough to provide a good explanation. Thank you in advance.

P.S. I am wondering why it doesn't have the dimensions ML2T-3...
 
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Well, a watt is a Newton-meter per second, so that's F D / T. And then hours is time, so it's F D T / T

(with conversion factors)
 
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russ_watters said:
Well, a watt is a Newton-meter per second, so that's F D / T. And then hours is time, so it's F D T / T

(with conversion factors)

Awesome. Thank you very much. I also figured something like this, as kWh is a unit of energy, it will ultimately equal the dimensions of energy, so the dimensions will be ML2T-2
 
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nineteen said:
Awesome. Thank you very much. I also figured something like this, as kWh is a unit of energy, it will ultimately equal the dimensions of energy, so the dimensions will be ML2T-2
Yes, it's just that the point of a kwh is that it has mixed time units, so I'm not sure if in this context it is useful to simplify or convert to base units (via f=ma). But sure, if that's what you are looking for...
 

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