I would write 8.0 with a dot over 0, in the same way we represent 1/3=0.3333... as 0.3 with a dot over 3. But I am not sure anyone would understand it.
Among the engineers I know, those who perform the best on quantitative finances are electrical engineers, but the sample size is small.
Search for "quantitative analyst" (in the case you didn't know this expression already). This may be the career your are looking for.
Try considering that the heat added is equal to the increment on internal energy of the water. Which are the initial conditions, the final temperature and the amount of heat per unit mass or unit quantity of matter?
Jd0g33,
∫ means a "sum" over differential amounts.
In ∫dE cosθ the differential amount is dE cosθ
dE is a vector and dE x cosθ is its projection on the x-axis.
Adding up all the projections of every dE, you get E_{x}.
When taking ∫y(x)dx, the differential amount being added up is...
256bits,
Thank you very much for your time!
Your hints on
"considering a control volume around the evacuated tank and considering the gas in the pipe as a system" and
"if you consider that a force on a mass can move the mass a distance x at constant velocity if there is an opposing force of...
I agree with you: "once some gas has entered the tank, any more gas entering into the tank has to do some work to compress that gas already in the tank." and this leads me to rephrase the objection (a) written above:
a) the gas filling the evacuated tank has to do some work to compress that...
Since the tank is an evacuated one, the gas entering the tank is submited to a free expansion, and during free expansion, no work is done by the gas, is it?
This is the example 2.12 from "Introduction to Chemical Engineering Thermodynamics", 6th. ed, by Smith, Van Ness & Abbott:
"An evacuated tank is filled with gas from a constant-pressure line. What is the relation between the enthalpy of the gas in the entrance line and the internal energy of...