# Tagged Questions

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### Heat equation : boundary conditions?

Say we have a bar centered at $x=0$, that is heated. We have the 1D Heat equation which we can solve to find a parabolic temperature profile : $$\kappa \frac{d^2 T}{d x^2}=-\frac{Q}{L S}$$ with ...
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### Derivation of cylindrical line heat source problem?

I have a line heat source embedded inside a cylinder and I am trying to find the temperature distribution T(r,t). By using the similarity variable, the solution to the differential equation is ...
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### Showing specififc internal energy $e$ is a perfect differential

I am reading a book on Gas dynamics and there is a small section on thermodynamics before the conservation laws of mass momentum and energy are introduced. The book says $$p = R \rho T$$ where ...
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### Problem involving 1st law of thermo and ideal gas law

Problem: $1.0 \text{ kg}$ of air at pressure $10^6 \text{ Pa}$ and temperature $398 \text{ K}$ expands to a five times greater volume. The expansion occurs such that in every instance the added ...
Here and here it states that water is at its highest density around $4^\circ$ Celsius. I know very little physics and a Google search has left me without an answer. I am teaching an ODE class in the ...