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19

Ice can be denser than water for certain values of $P,T$. Look at these two pictures taken from here: The darker areas in the second picture denotes areas of greater density. So you can clearly see that when pressure is increased, ice becomes denser than water along the coexistence line. For example at $T=400$ K ice VII is clearly denser than water ...


6

The temperature appearing the the Clausius inequality is definitely the temperature of the "boundary interface (with the surroundings)", or simply the temperature of the sources. One of the best places I have seen this discussion is in Fermi's book, chapter 5, section 11. He is explicit about it. To see this you have to recapitulate the steps in obtaining ...


4

$1$ litre of water will remain almost $1$ litre as long as it is in the liquid state, no matter what the temperature is. The following formula gives you an order of magnitude estimate of the expansion: $$\Delta V=V_0\ \Delta T \ \beta$$ where $\beta$ is the coefficient of thermal expansion and $V_0$ is the initial volume. For water, $\beta \approx 10^{-...


3

P-V work is not the only kind of work that can be done on the contents of your system. In the case of your fan example, the fan is doing work on the gas within the container by exerting force on it through a displacement (of the fan blade). The kinetic energy imparted to the gas by the fan is then converted to internal energy by viscous dissipation (a ...


3

You already have the answer when you write $$\frac{\Delta h}{h} = (\beta -2\alpha)\Delta T$$ What you do after that is unnecessary and does not make sense. You have already said that the height of the tube is irrelevant, so the height of the liquid "relative to the tube" is meaningless. If initially the liquid fills the tube completely and you want to ...


3

Whether an answer exists depends on your definition of "near" compared to STP. There are a few fluids that have their critical point at a temperature close to STP, but higher pressure. For example, (see http://www.engineeringtoolbox.com/critical-point-d_997.html) material Tc(K) Pc(atm) acetylene 309.5 61.6 ethylene 283.1 50.5 ethane ...


2

So, scientists were surprised when they found that Mercury has a molten core. Since small planets (like Mercury) cool rapidly, the core should've frozen a while ago. In a nutshell, though, whether or not the core stays molten over time depends on the composition of the core...as this website says, Maintaining a molten core over billions of years ...


2

The critical pressure is given by $$P_c=\frac{a}{27b^2},$$ while the critical temperature is $$T_c=\frac{8a}{27bR}=\frac{8bP_c}{R}.$$ The parameter $b$ is related to to the effective volume occupied by the molecules, $$b=4N_0V_0,$$ where $V_0$ is the volume of the molecule and $N_0$ is the Avogadro number. So at least theoretically you can chose $P_c=1\, \...


1

It is not true in general that liquids expand linearly with the temperature but it might be true for a particular liquid and a particular temperature scale. Let us say you have mercury. You put that Mercury inside your fridge and after some time you measure its volume and define this Mercury is at $0\, \mathrm{X}$, where $\mathrm{X}$ is the scale you are ...


1

Volume is not a meaningful measure of quantity, for the reason you hint at in your question. You can say how many moles (or grams) of water you drank - more useful if you want to know about the impact on your body chemistry. This is related to my answer about scales measuring in grams rather than Newtons. Can you see how?


1

Advantages Very accurate ( In fact its accuracy allows it to be utilised to calibrate other thermometers) Wide Range Independent of gas used Disadvantages Large and bulky(inconvenient to carry and handke) Slow to Respond (due high heat capacity) Expensive to manufacture and keep I'm not sure about its use in any specific industries.


1

I tried to look around but I couldn't find anything. It does seem like supercritical $\mathrm{CO_2}$ is very popular in applications because the critical temperature is just a little over $30^{\circ}\mathrm{C}$, but it still requires 73 atmospheres of pressure. An interesting thing mentioned on the Wiki page is that Venus may have had supercritical $\mathrm{...


1

Actually the formula given in your question describes the thermal efficiency $Nth$ of a device , usually a heat engine that transforms thermal energy into mechanical energy and it's always: $Nth<1$. On the other hand $COP$ or coefficient of performance is the ratio $Q/W$ of the device called heat pump, where $Q$ is the heat removed from the cold ...



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