Covers the study of (mostly homogeneous) macroscopic systems from a heat/energy/entropy point of view. Maybe combine with [tag:statistical-mechanics].

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Can ice thickness be different on two nearby lakes?

In winter, is it possible for two distinct bodies of water, which are a few kilometers apart (so they are exposed to roughly same temperature), to have different thickness of ice? Does the area of the ...
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3answers
5k views

Would a Cup of Tea Be Hotter If you Add the Milk Before or After Boiling Water?

This is a bit of dispute between work colleagues. An answer would be greatly appreciated. My argument is as follows: If you add X amount of milk at a temperature of M to a mug at room temperature R ...
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1answer
535 views

Understanding heat pump efficiency

I have read that heat pumps are more efficient than generating heat directly for heating homes, until the temperature gets down to a critical value. I just asked how to calculate temperature of ...
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105 views

Specific Heat of Nano Particles

Specific heat of nano particles is less than bulk specific heat of them. Why?
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115 views

Van der Waal's gas satisfies $U = \int_{0}^T C_VdT - a/V + K$ (constant)

I need to show that a Van der Waal's gas satisifes $$U = \int_{0}^T C_VdT - \frac{a}{V} + K$$ where $K$ is constant. The equation of state of a VDW gas is $$\bigg(p + \frac{a}{V^2}\bigg)(V - b) ...
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315 views

Computing the efficiency of a heat engine

With the heat engine we have an ideal gas working the substance. I want to show that the efficiency of this heat engine is $$\eta = 1 - \frac{1}{\gamma}\frac{\bigg(\frac{V_3}{V_1}\bigg)^\gamma - ...
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1k views

Net work output of an engine performing Carnot cycle?

My problem gives me a Carnot cycle heat engine with water as its working fluid, with $T_H$, $T_L$, and the fact that it starts from saturated liquid to saturated vapor in the heating process. I need ...
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399 views

Rate of Cooling

I was given the following problem: Two objects have a temperature difference of 20 degrees C at time 0. Two minutes later, they have a temperature difference of 18 degrees. How long does it take ...
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4answers
14k views

Formulae for Heat Change and Internal Energy Change in a Thermodynamic Process

Today, we were being given a lesson on Thermodynamics when my brain encountered an error. It is easy to derive that, $\Delta U$, the internal energy change for constant volume process is given by, $$ ...
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2answers
694 views

Order of phase transitions

I got to read things like In case of a first order phase transition, the volume and temperature change in a discontinuous manner. However for phase transitions of higher order the change in ...
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390 views

Rayleigh-Benard Convection

I found this nice paper about RB convection. However I am confused by what is going on page 6. In particular why we are suddenly using Helmholtz equation to find spatially periodic solutions. Aren't ...
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2k views

Why do some metal containers not conduct heat, while some do?

Some metal containers such as the Nissan Thermos ones, even if 100 C water is filled inside, the container is still cold to the touch on the outside. It won't be even warm: At the same time, some ...
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511 views

Which heated, partially filled bottle will explode first?

This is in reference to a pasteurization discussion on a homebrewing forum. I have four closed bottles which will explode if containing too much pressure. Two of them are 50% full (A and B), and two ...
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4k views

Calculating time to heat cold water in bowl of hot water

How would I calculate the time it takes to heat a given volume of water to a given temperature with a given temperature T1 when it is submerged in a volume of water with a temperature T2 Estimation ...
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2answers
410 views

Density of states via a Laplace transform

Is this formula correct? $$ \frac{-1}{\pi}Im\int_{0}^{\infty}\!dt~\exp(Et)\Theta (t)\exp(i \epsilon t) ~=~ \sum _{n}\delta (E-E_{n}), $$ $$ \Theta (t)~=~ \sum_{n}\exp(-tE_{n}) ,$$ and I have used ...
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727 views

Can we explain physical similarities between Black Scholes PDE and the Mass Balance PDE (e.g. Advection-Diffusion equation)?

Both the Black-Scholes PDE{*} and the Mass/Material Balance PDE have a similar mathematical form of the PDE which is evident from the fact that on change of variables from Black-Scholes PDE we derive ...
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2answers
313 views

What devices could be taken round dwellings to measure the thermal conductivities of buildings in situ?

Your lateral thinking and knowledge of lab kit could help us solve a tricky measuring problem in building-physics. One of the problems we get in modelling the heat demands of buildings, is getting an ...
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254 views

Physicality of claims regarding AC ice energy storage units

Many of us may remember the problems from thermodynamics where we had to determine if a pretend air conditioning unit supplier's claims violated the 2nd law. I want to pose a similar question ...
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38 views

When food cooks, does it gain energy?

I'm just thinking about roasting a chicken in the oven. The heat in the oven does work on the chicken to cook it, but is the same amount of energy dissipated from the oven as is put in, or is some ...
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36 views

Liquid/solid to plasma?

During a phase change we can go from solid to gas via the process of sublimation. The diagram given below indicates that there is no analogous process for the transition from solid (or liquid) to ...
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2answers
64 views

Book recommendation for nonequilibrium thermo/stat mech

I'm doing an undergrad research project that lies at the intersection of biology and nonequilibrium thermodynamics, but I'm starting to realize almost none of my equilibrium thermo/stat mech knowledge ...
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1answer
108 views

What exactly is entropy? Why is it measure of randomness? [duplicate]

What exactly is entropy? Why is it measure of randomness? I have been told Entropy is measure of randomness and it increases everytime randomness increases. What is Randomness? Randomness in what? ...
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37 views

RMS Speed of Gas Molecule for Polyatomic Molecules

Halliday in his book and also many people say that RMS speed, $v_{rms}$ is $\sqrt{\frac{3RT}{M}}$. However, he used this formula in showing that kinetic energy, $K$, is $\frac32kT$. but how about ...
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93 views

Why doesn't power generated by thermal radiation violate Carnot's theorem?

It seems to me that you could use thermal radiation to drive an engine that does not require a cold reservoir. Carnot's theorem states that the only way to convert heat into work is with a temperature ...
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57 views

Maximum Temperature?

I have been reading a lot about wavelengths of light and Planck's law and such. Curious as to whether a minimum wavelength of $h$ (Planck's Constant) indicates that there is in some way an absolute ...
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310 views

Simpler derivation of Sackur-Tetrode equation

Is there a reason the following derivation for the Sackur-Tetrode equation is not common? I am teaching a lower undergraduate level class and would like to derive it with simpler terms of only using ...
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79 views

Finding $p(z), \rho(z)$ of an ideal classical gas in a box

We have a classical ideal gas of particles of mass $m$ at fixed chemical potential $\mu$ and fixed temperature $T$. We have a potential energy $U(z)=mgz$ and the gas is in a rectangular box of height ...
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209 views

How to calculate liquid pressure regardless of the gravity?

Assume we have a balloon in a tank filled with a liquid , without any gravitational forces: We just know the Temperature, $V_0$ and $V_1$ I want to calculate the pressure exerted from the liquid on ...
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161 views

Thermodynamics of expanding nitrogen bubble as it rises in water

Problem An air bubble is released from a nitrogen tank 20 meters under water. The bubble has a radius of 1 mm. What will be the radius of the bubble when it reaches the surface? My Questions Is it ...
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126 views

Is there a “high temperature” variant of 0 degrees Kelvin? [duplicate]

I know that -273.15 degrees celsius, also known as Absolute Zero or 0K is the low temperature limit for objects, but is it possible that there is a 'highest temperature?' I would have to guess that ...
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3answers
146 views

Entropy of loops in the PV plane

The change in entropy of the Carnot and reversible cycles is said to be 0. Several other loops are supposed to have a non-negative change in entropy. This presents 2 problems which I cannot ...
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3answers
192 views

Interpretation of systems in different state of matters BUT almost identical configuration

For a start, let me clarify that by "almost identical configuration" I mean same volume, temperature and number of molecules (but different pressure). One could for instance take two identical systems ...
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410 views

How to calculate Gibbs free energy of diamond?

How the effect of crystal structure on Gibbs free energy is calculated? For example, how the Gibbs free energy of diamond is 2.9 kJ/mol, while that of graphite is 0?
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394 views

Are pressure and volume not independent properties in liquid water?

Every thermodynamics textbook teaches us that, for a simple compressible substance, any two independent properties will suffice to determine the system state. Those can be pressure and temperature ...
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74 views

Are temperature increases discrete? [duplicate]

Are temperature increases ever discrete in nature, or is it a continuous variable? If a discrete case exists, is there any material that exhibits particularly strange behavior?
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731 views

Why does the thermal conductivity of water decrease with increasing salinity?

Intuitively I would expect the thermal and electric conductivity to be positively related, and since electric conductivity increases with salinity, so should thermal. But according to this table ...
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135 views

paradoxical results in different applications of the 2nd law of thermodynamics

Assume two closed systems adjacent to each other together forming one adiabatic system. Both systems are assumed to have their volumes fixed and can therefore communicate with each other through heat ...
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3answers
272 views

Problems with units of entropy in statistical thermodynamics

The statistical thermodynamics definition of entropy: $S = kN \ln (W)$ troubles me a lot with the problem of dimenstions. where $S$ is entropy; $k$, the Boltzmann constant; $N$ the number of particles ...
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92 views

Is there an alternative metric for isentropic efficiency that remains valid when broken up into multiple segments?

Say that we have an irreversible expansion process which extracts energy, like a turbine. Isentropic efficiency is commonly defined by the following relation, which applies in a similar fashion for ...
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170 views

Why did everything in space cool out?

Through my research, I learned that; According to thermophysics, heat always moves from an area of high heat to an area of low heat. Space has no heat at all. It is extremely cold However, ...
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602 views

Flory-Huggins ternary phase diagram with a neutral component

I am searching the literature for the Flory-Huggins phase diagram with the following components : polymer, solvent, and a third component that does not interact with the other components (just entropy ...
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1answer
116 views

Thermodynamic relations

I'm asked to establish the following relations: $\left( \frac{\partial C_V}{\partial V} \right)_{T,N} = \frac{T}{N} \left( \frac{\partial^2 P}{\partial T^2} \right)_{V,N} $ $\left( \frac{\partial ...
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1k views

Why the dissolution of hydrophobic compounds decreases the entropy of water molecules in the vicinity of the solute?

The following is a quote from Lehninger's Principles of Biochemistry, 4th edition, pg.52: (...) dissolving hydrophobic compounds in water produces a measurable decrease in entropy. Water ...
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2answers
513 views

Are there critical constants for liquid-solid transition?

I'm aware of the critical constants for gas-liquid transition but is there such constants for liquid-solid transition? Like the maximum temperature above which a liquid cannot be solidified.
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1k views

Equation of state of a rubber band

I have the following question that I attached in png format. I have done part (a), but I am having difficulties in part (b) when I proceed according to the book. I have non zero tension at ...
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3answers
507 views

Why is gas(oline) in gas stations sold by volume (as opposed to mass)?

Fluids (including natural gasoline/petroleum) have variable volume based on the ambient temperature for the same mass of fluid. So, really, the amount of gas that you're filling your car with depends ...
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1answer
1k views

Diffusion of gas in a liquid with changing pressure and solubility (chemical potential)

Modelling the diffusion of a gas dissolved in water in a vertical column of water, several meters deep. Also assuming the water is completely still, so only diffusion plays a role. (Actually a model ...
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632 views

What is a chemical potential good for?

I read that the definition of the chemical potential is, that it is the partial derivative of the Free energy with respect to the number of particles, $$\mu=\frac{\partial F}{\partial N}.$$ ...
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2k views

Simple thermodynamics basics - can internal energy be calculated?

Well this got me stumbled, because I've been wondering what the "question" is. One of the example examns got the following question (strangely there are no supplied solution books): A $0.2 {\rm ...
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191 views

What are the largest thermal gradients achievable in a lab environment?

I am looking for a system capable of creating a gradient of $100\, \mathrm{K}/\mathrm{\mu \textrm{m}}$ on a $30\, \mathrm{\mu}\textrm{m}$ spacing of a system mounted on a Si-N membrane. My so-called ...