Basic physics units problems involving the Ideal Gas Law

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SUMMARY

The discussion centers on solving problems related to the Ideal Gas Law, specifically the equation pV = nRT, where R represents the ideal gas constant. The correct fundamental unit of R is identified as D. kg · m² · s⁻² · K⁻¹ · mol⁻¹. Participants also analyze the dimensional consistency of various equations involving acceleration, velocity, and time, concluding that choices B and C are possible while A, D, and E are not. Additionally, the typical mass of a tennis ball is confirmed to be 60 g, with participants calculating equivalent values in different units.

PREREQUISITES
  • Understanding of the Ideal Gas Law and its components (pressure, volume, moles, temperature).
  • Familiarity with dimensional analysis and its application in physics.
  • Basic knowledge of unit conversions in the metric system.
  • Ability to interpret and manipulate algebraic equations in physics.
NEXT STEPS
  • Study the Ideal Gas Law and its applications in real-world scenarios.
  • Learn about dimensional analysis techniques and their importance in physics problem-solving.
  • Explore unit conversion methods and practice converting between different mass units.
  • Review algebraic manipulation of equations in physics, focusing on dimensional consistency.
USEFUL FOR

Students studying physics, particularly those tackling problems involving the Ideal Gas Law, dimensional analysis, and unit conversions. This discussion is beneficial for beginners seeking to strengthen their foundational understanding of these concepts.

jamiebean
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Homework Statement


The following is the equation of ideal gas law, where p is pressure (Force/Area), V is volume, n is number of moles and T is temperature in Kelvin. What is the fundamental unit of R?
pV = nRT
A. kg^−1 · m^−2 · s^ 2 · K · mol
B. kg^−1 · m^−4 · s ^2 · K · mol
C. kg · m^4 · s ^−2 · K · mol^−1
D. kg · m^2 · s ^−2 · K^−1 · mol^−1
E. R is dimensionless

The fundamental unit of acceleration a is ms^−2 . Which of the following equations is/are impossible? Give a brief justification. (t is time, v is velocity and A, B and C are dimensionless constants)
A. a = A^−2BC^4 + v /t
B. a = Cv /t
C. a = v /t
D. a = v/ t ^2
E. a = t + v /t

Which of the following is the typical mass (60 g) of a tennis ball?
A. 6 × 10^4 mg
B. 60 × 10^−1 kg
C. 600 × 10^5 µg
D. 6000 × 10^−5 g
E. 60 000 × 10^5 ng

Homework Equations

The Attempt at a Solution


3:
I both calculated 60g in choice A and C
but there should only be 1 answer in this q. idk what happened.

2,1: because I am a starter, i have no idea how things work in these 2 q.
 
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Your calculations in 3 are correct. Both A and C amount to 60 g.
jamiebean said:
2,1: because I am a starter, i have no idea how things work in these 2 q.
I cannot interpret this. Can you translate in plain English?
 
kuruman said:
Your calculations in 3 are correct. Both A and C amount to 60 g.

I cannot interpret this. Can you translate in plain English?
sorry for my bad eng. in other words, i don't know how to calculate question 1 and 2.
 
Are you familiar with dimensional analysis? Most textbooks deal with it in chapter 1. Read your textbook about it and see here for another example
https://www.physics.uoguelph.ca/tutorials/dimanaly/
 
kuruman said:
Are you familiar with dimensional analysis? Most textbooks deal with it in chapter 1. Read your textbook about it and see here for another example
https://www.physics.uoguelph.ca/tutorials/dimanaly/

in q2,choice B and C are possible. But I am not sure if choiceA,D,E are possible or not
 
jamiebean said:
in q2,choice B and C are possible. But I am not sure if choiceA,D,E are possible or not
Can you state the reasoning you've used (so far) to reach the above conclusions?
What rules of dimensional analysis have you invoked?
 

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