Dimensional Analysis

dan4loriel

1. The problem statement, all variables and given/known data

how do i deduce the dimension of the following using dimensional analysis

Power enthropy, surface charge density, inductance, permitivity, radius of gyration



tried deducing the dimension of power like this:

p=work done/time
work done w= force x distance
=MLT e^-2 L
=ML e^T e^-2

substitute for power P= ML e^2 T e^ -2/T = ML e^ 2 T e^ -2

=ML e^ 2 T e^ -3

anyhelp will be appreciated

BruceW

I'm not sure what the 'e' is supposed to mean? Do you mean p = ML²T^-3 ? If this is what you meant, then you are correct for the dimensions of power.

dan4loriel

yes that is what i mean can you give me a clue on the dimension of enthrophy th3n

BruceW

do you mean entropy? And to figure out its dimensions, you just need to do the same kind of thing you did with power. You knew that power is energy divided by time, and you knew the dimensions of energy and time, so you just substituted them into the equation to get the dimensions of power. So what equations do you know which involve entropy?

dan4loriel

yes entropy, and i think dq=du+dw involves entropy am i right?

BruceW

ah, well not that equation exactly. but there is an equation which relates a small change in entropy to dq

dan4loriel

so what the equation please

BruceW

well the equation has dq, T and ds (small change in entropy). Have you been taught this equation yet? Do you know any other equations involving entropy? It seems strange that your teacher would ask for the dimensions of entropy if the class has not yet been introduced to the concept yet..