# Tag Info

19

Typically: $\rm d$ denotes the total derivative (sometimes called the exact differential):$$\frac{{\rm d}}{{\rm d}t}f(x,t)=\frac{\partial f}{\partial t}+\frac{\partial f}{\partial x}\frac{{\rm d}x}{{\rm d}t}$$This is also sometimes denoted via $$\frac{Df}{Dt},\,D_tf$$ $\partial$ represents the partial derivative (derivative of $f(x,y)$ with respect to $x$ ...

15

The reason is the same as why a metal pipe feels colder than wooden plank at the same temperature: thermal conduction. The heat from your tongue (including the moisture) is absorbed faster than your body can replenish it. This has the effect of freezing your saliva in the tongue's pores to the metal surface (which itself isn't too smooth at small scales). ...

8

You might get an order of magnitude estimate as follows. We make the rough assumption that everything ends up in its vessel as a monoatomic ideal gas - actually it will be a plasma, with a thermal energy per mole of $\frac{3}{2}\,R\,T_{final}$, where $T_{final}$ is the thermodynamic temperature of the plasma. Neglecting heats of vaporisation (we assume ...

4

1 You could find a relation between C and T from the assumptions(quarter of an ellipse) and just substitute that in the integral $$m\int C dT$$ 2 We usually say specific heat capacity of metal is some value at particular temperature and pressure say ( Standard Temperature and Pressure ). When we know that the specific heat changes with temperature ...

3

The answer depends on many factors, but here are the basic bits of physics that play: The power and wavelength of the laser The reflectivity of the surface (function of wavelength of the laser) The size of the focal spot The thickness of the sheet The thermal conductivity of the sheet The reflectivity of the copper is a particularly important one. If you ...

3

First, I want to say that different people use different notation and I welcome any comments. I also feel as if I am about to enter a minefield. Here the answer is made up with examples of use of $d$, $\partial$ and $\delta$. I would say for $d$ that $dV \over dx$ would be the total derivative in one dimension for $V(x)$ where the potential $V$ is a ...

2

I guess you refer to the free expansion of a gas, which is an irreversible process. During free expansion, no work is done by the gas. The gas goes through states of no thermodynamic equilibrium before reaching its final state, which implies that one cannot define thermodynamic parameters as values of the gas as a whole. For example, the pressure changes ...

2

The formula is actually better written $$\Delta S = \frac{Q}{T}.$$ That is, the change in entropy associated with the flow of heat is inversely proportional to the temperature at which the heat flow occurs. Note that $Q$ is already a change itself: it is not a state variable, but rather something more like $\Delta W$. Physically, this is because adding ...

2

1-How much energy(in calories) do we need to change the temperature of 1 kilogram of metal A from 0 to 40 Celsius? You simply integrate your function (find the area under the graph). I guess, what you have on the y-axis is $c=\frac{Q}{m \Delta T}$. Integrating gives you the amount of energy per mass, $Q/m$. 2-How can we choose a single value (as an ...

1

yes, the collisions between molecules in the gas and or walls in the container can change both the kinetic energy and the direction of motion, like millions of billiard balls moving in a huge pool table. The analogy with the billiard ball is not that good because the billiard balls will eventually end up at rest, as many collisions are inelastic and there ...

1

Since $n=\left(n_1,\,n_2,\ldots\right)$ with each $n_i\in\{0,\,1,\,2,\,\ldots\}$, then you can write the sum as $$\sum_{n_\alpha}=\sum_{n_1\in\{0,\,1,\ldots\}}\sum_{n_2\in\{0,\,1,\ldots\}}\cdots\sum_{n_m\in\{0,\,1,\ldots\}}$$ while your product is, $$\prod_\alpha e^{n_\alpha \beta}=e^{n_1\beta}e^{n_2\beta}\cdots e^{n_m\beta}$$ Thus, we have $$... 1 The specific heat of a molecule depends on the number of degrees of freedom the molecule has. There are several degrees of freedom available: translation (3), rotation (3), vibration (depends on the number of bonds in a molecule) and electronic modes. Now, for something that is monatomic, you have 3 translational modes (x,y,z directions), zero rotation ... 1 Well it all depends on what assumptions you are able and willing to make. For a start you can work out how much of the laser light is reflected. The reflected power will be something like (for normal incidence)$$\frac{P_{r}}{P_i} = \frac{(\eta_m - \eta_{vac})^{2}}{(\eta_{vac} + \eta_m)^2}, where $\eta_{vac}=377$ Ohms and $\eta_m$ is the impedance of the ...

1

It's a sum over states. The partition function can also be written as \begin{align} Z = \sum_\alpha g_\alpha e^{-\epsilon_\alpha/kT} \end{align} where $\alpha$ is an index which labels levels, $\epsilon_\alpha$ is the energy of level $\alpha$, and $g_\alpha$ is the degeneracy of level $\alpha$. This follows from the sum over states by noting that in that ...

1

A formula such as this (being a analog to parallel electrical resistors, as pointed out in the comments) can get a little more complicated when different areas are involved. However, I think that the author of your formula restricted the discussion to one single heat transfer area in order to avoid dealing with that. The heat transfer rate originally starts ...

1

When opening the bottle in space, all the air that was initially in it will flow out due to the pressure difference. The inside of the bottle will then become approximatelly vacuum, so when you open it on Earth air will flow in it again. (Unless it's not sturdy enough (for example a plastic bottle), in which case it will be compressed/crumpelt before you ...

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