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}...
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...
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...