Check the dimensional correctness of PV = Fx
Pressure times volume equals work. Pressure times volume has the dimension of work, force times distance.
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
P V = F xPV[M L2 T-2]=Fx[M L2 T-2]Step by step
1. What each symbol stands for
- P pressure [M L-1 T-2]
- V volume [L3]
- F force [M L T-2]
- x displacement [L]
2. The dimensions of each term
- PV [M L-1 T-2] × [L3] [M L2 T-2]
- Fx [M L T-2] × [L] [M L2 T-2]
3. Compare
Every term has dimensions [M L2 T-2], so the equation is dimensionally consistent.
What it proves and what it does not
It can show
- Every term that is added or subtracted has the same dimensions, so the sum makes sense.
- Both sides of the equals sign have the same dimensions.
- Angles inside sin, cos and similar functions are pure numbers.
It cannot show
- A pure number such as 1/2 or 2π has no dimensions, so a check cannot see a missing or wrong one.
- Two quantities with the same dimensions, such as work and torque, cannot be told apart.
- A sign error or a wrong power that keeps the dimensions equal goes unnoticed.
Matching dimensions are necessary but not sufficient. Pure numbers such as 1/2 or 2π have no dimensions, so a check cannot see them, and an equation with matching dimensions can still be wrong.
Look up each quantity
PV = Fx: quick answers
Is PV = Fx dimensionally correct?
Yes. Every term has the same dimensions, [M L² T⁻²], so PV = Fx is dimensionally consistent. That does not prove the equation itself is correct.
Does a dimension check prove PV = Fx is right?
No. A check can show that an equation is wrong, but it cannot show that it is right. Pure numbers such as 1/2 and 2π have no dimensions, so the check cannot see them.