Search results for query: *

This will transform the PDE into a wave equation. But this exercise asks to solve this problem not using this coordinate transformation. Thanks for your suggestion anyway.

Homework Statement Find out the Green's function, ##G(\vec{r}, \vec{r}')##, for the following partial differential equation: $$\left(-2\frac{\partial ^2}{\partial t \partial x} + \frac{\partial^2}{\partial y^2} +\frac{\partial^2}{\partial z^2} \right) F(\vec{r}) = g(\vec{r})$$ Here ##\vec{r}...

I was looking for a rigorous derivation.

Homework Statement Suppose two successive coordinate rotations through angles ##\Phi_1## and ##\Phi_2## are carried out, equivalent to a single rotation through an angle ##\Phi##. Show that ##\Phi_1##, ##\Phi_2## and ##\Phi## can be considered as the sides of a spherical triangle with the angle...

Homework Statement In the case of a gas obeying the equation of state $$\begin{align}\frac{Pv}{RT}&=1+\frac{B}{v}\end{align} $$ where ##B## is a function of ##T## only, show that, $$\begin{align}c_v&=-\frac{RT}{v}\frac{d^2}{dT^2} (BT)+\left(c_v\right)_0\end{align}$$ where ##\left(c_v\right)_0##...

Could you please explain this part? The heat capacity for ideal gas is a constant while for van der waals gas, it is a function of temperature. What did you actually mean by they are identical?

Homework Statement Show that for a gas obeying the van der Waals equation ##\left(P+\frac{a}{v^2}\right)(v-b)=RT##, with ##c_v## a function of ##T## only, an equation for an adiabatic process is $$T(v-b)^{R/c_v}=constant$$ Homework Equations ##TdS=c_vdT+T\left(\frac{\partial P}{\partial...

Thanks for pointing out the mistake. I am used to solve problems for ideal gases, that's why I have made the mistake, I guess. Thanks for the hints! ##dQ_R=TdS=T\left(\frac{\partial S}{\partial T}\right) _V dT + T\left(\frac{\partial S}{\partial V}\right) _T dV ## So, we have to show that...

I tried as you mentioned, ##\left(\frac{\partial C_V}{\partial V}\right)_T## ##=\left(\frac{\partial}{\partial V}(T\left(\frac{\partial S}{\partial T}\right)_V)\right)_T## ##=T\left(\frac{\partial}{\partial V}(\left(\frac{\partial S}{\partial T}\right)_V)\right)_T## ... (i) Now...

Homework Statement ##dz=Mdx+Ndy## is an exact differential if ##(\frac{\partial M}{\partial y})_x=(\frac{\partial N}{\partial x})_y##. By invoking the condition for an exact differential, demonstrate that the reversible heat ##Q_R## is not a thermodynamic property. Homework Equations...

Homework Statement Derive the equation ##U=-T(\frac{\partial A}{\partial T})_V## where ##U## is the internal energy, ##T## is the temperature, ##A## is the Helmholtz function. Reference: Heat and Thermodynamics, Zemansky, Dittman, Page 272, Problem 10.4 (a) Homework Equations ##dA=-PdV-SdT##...

Homework Statement A long metal pipe of square cross-section is grounded on three sides, while the fourth (which is insulated from the rest) is maintained at constant potential ##V_0##. What is the electric field just outside the section opposite to ##V_0##? Homework Equations The Attempt at...