Since it represents the useful work, I take it to be the extra energy to be provided or the energy released after comtribution from the environment.##[-\Delta(TS)]##
Most questions we have on Gibb's Energy are either on spontaneity, or application of that formula in isothermal case.##\Delta G=\Delta H-T\Delta S##
##\Delta H=\Delta U +\Delta n_gRT##
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Unless you are referring to calorimetry of mixtures,(calculating final temperature given the value...
So the formula I learned in chemistry $$\Delta G=\Delta H-T\Delta S= \Delta U+\Delta(PV)-T\Delta S$$ is only for isothermal cases??
Since I have used it for reactions in chemistry, most chemical reactions are isothermal??
And since products and reactants are different compounds that would...
If ##d## represents a small change and ##\Delta## represents a large change
Why does the formula change from $$dG=dU+d(PV)-d(TS) \text{ for small change }$$
To $$\Delta G=\Delta U+\Delta(PV) -T\Delta S \text{ for big change}$$
How do you get this??
Shouldn't it be:
If ##\Delta G=\Delta H-T\Delta S##
Then ##dG=dH-TdS## (Small Change)
Also if ##\Delta H=\Delta U+\Delta(PV)##
Then ##dH=dU+d(PV)=dU+VdP+PdV##
##dU=0##
Finally $$dG=VdP+PdV-TdS$$
Correct?
So I had to find change in entropy of system in reversible isothermal process.
$$T\Delta S_{sys.}=Q\implies \Delta S_{sys.}=nRln\left(\frac{V_2}{V_1}\right)$$
This was good because for isothermal process ##\Delta U=0\implies Q=W##
Then I read this
Throughout an entire reversible process, the...
Won't that hole affect the potential (since it affects field)?
Here the potential of the shells is calculated without accounting for the hole. So value of induced charge on inner sphere is wrong and therefore the rest of the calculations are wrong??
This helps to find capacitance without finding induced charges or potential on the spheres.
But there also questions that ask to find charge on inner sphere which causes the problem I asked in the title
So a metallic Earth without a metallic Ionosphere is not possible.
Also won't the hole affect the potential?
This is how I was shown to find the potential and then capacitance:
$$\frac{KQ}{b}+\frac{Kq}{a}=0\implies q=\frac{-Qa}{b}$$
Then potential difference$$=\frac{KQ}{b}-\frac{KQa}{b^2}$$...
Why though? Why should grouunding the inner sphere cause any problem to the outer sphere? It's still a metal and therefore charge will dustribute to get to maximum distance from each other right?
That gives us the capacitance. A fixed value of capacitance means a charge corresponding to that must be on the inner sphere( ##\neq 0##) which got there without an electric field ❗️ 🤔
Even in current electricity the motion of charges is explained by field developed due to emf of cell.$$I=nAev_d=nAe\left(\frac{eE}{m_e}\tau\right)$$
In this question as well, the explanation for why capacitor opposes current flow in charging is that the field for finite area charged sheet is...
So from Gauss theorem, electric field at any point inside a uniformly charged sphereical shell is zero. Thus there is no electrostatic force on the inner sphere.
From what I have learnt, a field is necessary to move charges. But in this case the inner sphere acquires a charge q without any...