Linked Questions

0
votes
1answer
760 views

Find dimensional formula of $\alpha$ [duplicate]

The power delivered by a force is given by the relation $$P=\frac{\alpha}{\beta}e^{-\beta t},$$ where $t$ is time. Find the dimensional formula for $\alpha$. So, $-\beta t$ doesn't make sense for the ...
3
votes
2answers
203 views

Is it a problem that you can write the logarithm of a quantity with units? [duplicate]

While working out something in thermodynamics, I encountered an equation that had a term like $\log(n_1/n_2)$, where, $n_1$ and $n_2$ are the number densities. Now of course the argument of the $\log$ ...
0
votes
1answer
37 views

Dimensions in the logarithmic form of the Arrhenius equation [duplicate]

The logarithmic form of the Arrhenius equation is: $\displaystyle\ln k=\ln A-\frac{E_a}{RT}$ Here $k$ and $A$ have dimensions whereas $\displaystyle\frac{E_a}{RT}$ is dimensionless. In other words, $...
82
votes
6answers
14k views

Why is it “bad taste” to have a dimensional quantity in the argument of a logarithm or exponential function?

I've been told it is never seen in physics, and "bad taste" to have it in cases of being the argument of a logarithmic function or the function raised to $e$. I can't seem to understand why, although ...
67
votes
10answers
5k views

Should zero be followed by units? [duplicate]

Today at a teachers' seminar, one of the teachers asked for fun whether zero should be followed by units (e.g. 0 metres/second or 0 metre or 0 moles). This question became a hot topic, and some ...
47
votes
12answers
14k views

Why are angles dimensionless and quantities such as length not?

So my friend asked me why angles are dimensionless, to which I replied that it's because they can be expressed as the ratio of two quantities -- lengths. Ok so far, so good. Then came the question: ...
51
votes
5answers
6k views

Fundamental question about dimensional analysis

In dimensional analysis, it does not make sense to, for instance, add together two numbers with different units together. Nor does it make sense to exponentiate two numbers with different units (or ...
13
votes
3answers
9k views

Exponential or logarithm of a dimensionful quantity?

I have a unit measure, say, seconds, $s$. Furthermore let's say I have a dimensionful quantity $r$ that is measure in seconds, $s$. What is the unit measure of $e^r$? ($1/r$ is in $Hz$.) My question ...
24
votes
2answers
1k views

Why are expressions such as $\operatorname{ln}T$ used in thermodynamics where $T$ is not dimensionless?

In all thermodynamics texts that I have seen, expressions such as $\operatorname{ln}T$ and $\operatorname{ln}S$ are used, where $T$ is temperature and $S$ is entropy, and also with other thermodynamic ...
7
votes
3answers
10k views

Is a vector and a unit vector dimensionless

Lets say I have a position vector $\vec r$. Is it dimensionless or does it have a dimension of length i.e $[L]$. Also does the unit vector $\hat r$ have a dimension?
0
votes
1answer
5k views

What does really mean by- power of a number or an exponential function is dimensionless? [duplicate]

Is power of only a number or an exponential function is dimensionless? If power of any other thing can also be dimensionless then please explain with examples.
1
vote
3answers
202 views

Dimensional analysis - application to logarithms

I read some nice threads about this topic: physics StackExchange maths StackExchange stats StackExchange However, it still puzzles me that logarithm of some physical quantity has no units. Example, ...
2
votes
1answer
178 views

Dimensional Analysis : Thermodynamics

I was coming across some notes online for phase transitions. In one of the places, the author has written the Claussius-Clayperon equation in this form, $$ \frac{d(ln P)}{d(ln T)} = \frac{T\Delta S}{...
0
votes
2answers
192 views

How do I decide dimensions of a logarithmic function?

How do I decide the dimensions of a trigonometric quantity and a logarithmic quantity? For example, what are the dimensions for: $$\frac{C}{B} = \frac{D^2}{A} + \log \left(\frac{AC}{BD}\right)$$
4
votes
1answer
50 views

Why this constant is included in the tortoise coordinate?

In the Schwarzschild spacetime, the tortoise coordinate $r_\ast$ is defined by the property that $$\dfrac{dr_\ast}{dr}=\left(1-\dfrac{2M}{r}\right)^{-1}$$ Now, we cam integrate this. Multiply by $r$ ...

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