# Basic physics units problems involving the Ideal Gas Law

• jamiebean
In summary, the ideal gas law equation is pV = nRT and the fundamental unit of R is kg · m^2 · s^-2 · K^-1 · mol^-1. The typical mass of a tennis ball is 60 g and both choices A and C are correct answers. In question 2, choices B and C are possible based on dimensional analysis, but it is unclear if choices A, D, and E are possible without further information.
jamiebean

## 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

## 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.

Last edited by a moderator:
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?

## What is the Ideal Gas Law and how is it used in physics?

The Ideal Gas Law is a formula that describes the relationship between the physical properties of an ideal gas, including pressure, volume, temperature, and number of moles. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. This law is used in physics to solve problems involving gas behavior under different conditions.

## What are the basic units used in the Ideal Gas Law?

The basic units used in the Ideal Gas Law are pressure (P) in Pascals (Pa), volume (V) in cubic meters (m^3), temperature (T) in Kelvin (K), and number of moles (n) in moles (mol). The gas constant (R) can be expressed in different units depending on the specific values used in the problem, such as Joules per mole Kelvin (J/molK) or liters atmospheres per mole Kelvin (L atm/molK).

## How do I convert from Celsius to Kelvin in problems involving the Ideal Gas Law?

To convert from Celsius (°C) to Kelvin (K), you can use the formula K = °C + 273.15. This is because the Kelvin scale starts at absolute zero, which is -273.15°C. Therefore, adding 273.15 to the temperature in Celsius will give the equivalent temperature in Kelvin.

## What is the relationship between pressure and volume in the Ideal Gas Law?

According to the Ideal Gas Law, pressure (P) and volume (V) have an inverse relationship. This means that as one increases, the other decreases, and vice versa. This relationship is also known as Boyle's Law, which states that at a constant temperature, the product of pressure and volume remains constant.

## How can I use the Ideal Gas Law to solve for an unknown variable?

To solve for an unknown variable in the Ideal Gas Law, rearrange the formula to isolate the variable you are looking for. For example, if you need to solve for volume (V), the formula can be rearranged to V = nRT/P, where n, R, and P are known values. Plug in the known values and solve for V.

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