How to Use SI Units in Equations for Scientists

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SUMMARY

This discussion focuses on the proper use of SI units in scientific equations, particularly in the context of dimensional analysis. Participants emphasize the importance of consistently carrying units throughout calculations to ensure accuracy and clarity. A specific example involving the calculation of cooling water mass in a nuclear power plant scenario is provided, illustrating the necessity of including unit conversions, such as converting kilojoules to joules. The consensus is that understanding and applying dimensional analysis is crucial for solving problems correctly.

PREREQUISITES
  • Understanding of SI units and their significance in scientific calculations
  • Familiarity with dimensional analysis techniques
  • Basic knowledge of thermodynamics, particularly heat transfer equations
  • Ability to perform unit conversions, such as kJ to J
NEXT STEPS
  • Study "Dimensional Analysis" to grasp its application in various scientific problems
  • Learn about "Thermal Energy Calculations" using the equation E = mcΔT
  • Explore "Unit Conversion Techniques" for effective problem-solving in physics
  • Review "Specific Heat Capacity" values and their applications in real-world scenarios
USEFUL FOR

This discussion is beneficial for students in physics or engineering, educators teaching scientific principles, and anyone involved in calculations requiring precise unit management and dimensional analysis.

CSPTT
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Hi Everyone,
I think I posted this message to the wrong forum, so second try... I hope this is the right one? Could someone please explain to me how I know when to use SI units to solve a problem and how to enter these units into an equation - are there any rules of thumb? If I could get a sample equation with an explanation that would be great, but any kind of help is welcome! (My teacher only refers me back to the book and the book doesn't explain anything, it only gives me the tables... )
Many thanks,
CSPTT
 
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Please do not post multiple threads. I'm afraid I do not understand your question, do you mean dimensional analysis? Checking whether the units of an answer makes sense?
 
In general, when you do any calculation... you should include the units of the number along with the number itself, and this includes looking at the units of any constants that may be in the equations you choose to use (if you look in theback of the text, constants often have a different "numbers" tabulated for different units). Within a calculation, the unit dimensions you use should be consistent between all chosen constants and entered values. The nice thing about carrying along the units is that then you will know the units of your answer... which is always a good check to see if your answer makes sense.

You do want to look up more on "dimensional analysis" as Hootenanny suggests.
 
CSPTT said:
Hi Everyone,
I think I posted this message to the wrong forum, so second try... I hope this is the right one? Could someone please explain to me how I know when to use SI units to solve a problem and how to enter these units into an equation - are there any rules of thumb? If I could get a sample equation with an explanation that would be great, but any kind of help is welcome! (My teacher only refers me back to the book and the book doesn't explain anything, it only gives me the tables... )
Many thanks,
CSPTT
Welcome to TT. The choice of mks or cgs units is pretty much up to the textbook and the class instructor, but carrying units through your work is fundamental. Here is a recent thread where we talked about the value of consistent units and how it can help your work:

https://www.physicsforums.com/showthread.php?t=130989
 
Hootenanny said:
Please do not post multiple threads. I'm afraid I do not understand your question, do you mean dimensional analysis? Checking whether the units of an answer makes sense?
Many thanks for your answer and I'm sorry I posted twice - I did not know my messages would be moved to the right place by the administrators... Anyway, here is a problem and the equation to solve it where I got stuck because I did not know I had to add the number for the unkown SI unit included. I add comments on exactly what I did not understand at the end:
problem - the excess heat of a nuclear power plant is 1.5 GW. It is carried away by cooling water, which is made 10°C warmer in the process. How much cooling water is used in 1 s?
equation - 1.5*10^9*1.0=4.18*10^3*m*10
m=36*10^3 kg
I did not know I had to add the number for the SI unit in question and also, once I did realize it had to be added, I had no idea WHERE in the equation it should go. So my question is: how does one know? Are there any general rules for when to include the numbers of an SI unit and for where to put them in the equation?
CSPTT
 
physics girl phd said:
In general, when you do any calculation... you should include the units of the number along with the number itself, and this includes looking at the units of any constants that may be in the equations you choose to use (if you look in theback of the text, constants often have a different "numbers" tabulated for different units). Within a calculation, the unit dimensions you use should be consistent between all chosen constants and entered values. The nice thing about carrying along the units is that then you will know the units of your answer... which is always a good check to see if your answer makes sense.

You do want to look up more on "dimensional analysis" as Hootenanny suggests.
Thank you so much for clarifying that! There is just one other thing: if you have an equation where the SI unit in question is not given, but is part of the answer when solving "m", does the same reasoning apply - should I always assume that I have to add the number for the SI unit in question as well as the unit - so that if the unit is kg I have to add 10^3 into the equation? And if so, how do I know where in the equation 10^3 should go (the equation I had trouble with is posted above in the reply to Hootenanny)?
 
berkeman said:
Welcome to TT. The choice of mks or cgs units is pretty much up to the textbook and the class instructor, but carrying units through your work is fundamental. Here is a recent thread where we talked about the value of consistent units and how it can help your work:

https://www.physicsforums.com/showthread.php?t=130989
Thank you! And the thread was very interesting! Good to know that there are shortcuts to remembering the formulas :-) If you have time, I hope you would take a look at my answer to Hootnanny above, though, where I include the actual problem and equation that confuse me - I should have added them right away in my first post, but didn't think... Anyway. This forum is great.
CSPTT
 
What equation are you using for the temperature rise of the water? Can you please show the full equation with units for each quantity?
 
berkeman said:
What equation are you using for the temperature rise of the water? Can you please show the full equation with units for each quantity?
E=c*m*delta T - here are the full details for the answer that the teacher gave: c for water=4.18 kJ/(kg*C°)
density for water=1.0*10^3 kg/m^3
V=m/rho (the small p-sign, the Greek sign for r)=36*10^3/1.o*10^3=36 m^3
Thank you for taking a look at it!
CSPTT
 
  • #10
You're getting closer. 1GW power input for 1s raises a volume of water by 10C. Can you show your work on how you calculated m from your first equation?
 
  • #11
1.5*10^9*1,0 = 4.18*m*10
Because I did not know I had to add the 10^3 thing, as the kg would be the unknown in m - or so I figured and I'm still not quite sure why that is wrong...
CSPTT
 
  • #12
The problem is that you keep dropping units from your calculation. You *need* to carry units along with the numbers, in order to avoid missing things like kJ versus J and so on. Do it more like this:

E = Power * time = c m \Delta T

1.5 * 10^9 W * 1s = 1.5 * 10^9 J = c m \Delta T

1.5 * 10^9 J = 4.18 [\frac{kJ}{kg C}] m [kg] 10 [C]

Now solve the equation for m, being careful about units. Like how do you handle J on the left and kJ on the right...?
 
Last edited:

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