1
vote
0answers
41 views

Why can I calculate the value of an energy quantum of an Einstein solid at half the equipartition value of the heat capacity?

The energy quantum of an Einstein solid (in the limit of classical mechanics for one dimension, disregarding internal structure) can be calculated by estimating the value of $kT/\epsilon$ when ...
1
vote
1answer
22 views

Followup to: The relation between energy quanta of an Einstein solid and the equipartition value of heat capacity

As a followup question to this question: The relation between energy quanta of an Einstein solid and the equipartition value of heat capacity and this answer ...
2
votes
1answer
34 views

The relation between energy quanta of an Einstein solid and the equipartition value of heat capacity

Consider an Einstein solid with quantized energy values $U=q\epsilon$ and $N$ oscillators. I calculated some values of an Einstein solid numerically through a function in R (at the bottom of the ...
1
vote
0answers
10 views

What are the thermal properties of a “perfectly rigid” container?

can a "perfectly rigid" container be a diathermal boundary? I checked the wikipedia article for heat and read: Kinetic theory explains transfers of energy as heat as macroscopic manifestations of ...
0
votes
0answers
35 views

Thermodynamic potentials: Demonstration [on hold]

I must prove whether the statement on bold is true or wrong. Under it there is what I tried, but it does not convince me. I use one maxwell relationship on the latest line. And I take advantage of ...
0
votes
0answers
31 views

How to solve this steady flow problem? [closed]

Consider a steady Flow of air through a insulated porous plug. Air enters the plug at 100 kPa and 150m/s and leaves the plug at 50 kPa. Assuming air to be ideal gas and neglect potential energy ...
0
votes
0answers
32 views

A problem of thermodynamics [closed]

A lake is covered by a block of ice 10 cm thick. The water temperature is 0ºC and -5ºC for the air above. Calculate the ice growth rate of the block dx/dt knowing that the latent heat of fusion is ...
0
votes
0answers
33 views

Quadratic versus other types of degrees of freedom

In my text book I have the following question and after thinking about this one for hours, I can't figure out what they're getting at: In Section 2.5* I quoted a theorem on the multiplicity of any ...
1
vote
1answer
34 views

Partial Pressure - Which solution is right?

Question: Carbon dioxide (1.100 g) was introduced into a 1.00 L flask which contained some pure oxygen gas. The flask was warmed to 373 K and the pressure was then found to be 608 mmHg. If CO2 and O2 ...
1
vote
1answer
43 views

Irreversible work

I'm having some trouble trying to find the irreversible work done by a perfect gas when expanding. I know that the reversible work is greater than the irreversible one, but how can I find the ...
2
votes
2answers
41 views

Problem regarding heat engines [closed]

We have two different set ups: A 200K brick in a 300K environment A 300K brick in a 200K environment From which one of these can you extract more work? Assume equal mass and heat capacity. Using ...
0
votes
1answer
33 views

Calculating height and evaluating the vicinity of a peak in a multiplicity function for a two-state paramagnet

I have to calculate the height and width of the multiplicity function for a two-state paramagnet. I'm supposed to do this analogously to the method in the text book, which I will try to outline below. ...
1
vote
0answers
36 views

Heat transfer to a cube from one of the faces [closed]

Heat Flux= 10 MW Inlet water temperature = 28 degree centigrade for cooling purpose through a tube passing through the centre of retangular block of length 50 mm,height 30 mm and width 30 mm inner ...
3
votes
1answer
97 views

Entropy of a two-level system

Consider a two-level system with energies and degeneracies $\epsilon_0 = 0, g_0=1$ and $\epsilon_1 = \epsilon, g_1=4$. I can show that the temperature at which both levels are equally populated is ...
2
votes
1answer
43 views

Gas pressure and centrifugal force

I think about a rotating torus (simplified tire) filled with ideal gas. Mass of gas is $m$ and molar mass is $M$. Pressure in non rotating torus is $p_0$. Temperature is constant $T$. Inner radius of ...
1
vote
0answers
40 views

Supercritical Steam Expansion [closed]

Ten kg of steam at 500 bar is expanded at constant pressure until its volume increases to seven times its initial value of 0.01 $m^3 $. (a) Calculate the initial and final temperature of the steam ...
2
votes
1answer
49 views

Power required to keep a freezer at constant temperature

Alright, I'm completely stuck on this and so is everyone else I've asked. A freezer has a temperature Tc = -23℃. The air in the kitchen has a temperature Th = 27℃. The freezer in not perfectly ...
0
votes
0answers
26 views

Thermal Conduction through sphere

In general, a sphere with conductivity $\kappa$, heat capacity per unit volume $C$ and radius $R$ obeys the differential equation at time t: $$C\frac{\partial T}{\partial t} = \kappa \frac{\partial^2 ...
2
votes
1answer
62 views

Would it really require 44 car batteries to heat my pool? [closed]

After doing some research and math, I 'discovered' that it would take 44 (give or take 20%) car batteries to heat 1,000 gallon pool by 10 degrees. Is this right or am I missing something? It seems a ...
1
vote
1answer
64 views

Calculation of the differential of the entropy

In this review (for those who wants a precise reference see page 8 eq 21), the Author says that: \begin{equation*} S=-\sum_{i}P\left(i\right)\ln P\left(i\right) \end{equation*} and using the ...
1
vote
0answers
63 views

Thermal expansion of two bolts

I have this question asking me about the thermal expansions of two bolts, a steel one, and a brass one. I have the equation: $\ (\delta L/L)/T = \alpha $ I don't understand how I can use this ...
0
votes
2answers
79 views

The entropy of the universe in an irreversible cycle [closed]

Suppose we have an ideal gas performing an irreversible cycle composed by: an isothermal transformation at $T_{1}$; an isobaric transformation at $P_{A}$; an isothermal transformation at $T_{2}$; an ...
0
votes
0answers
21 views

If maximal work is extracted, in what manner does the heat flow between bodies?

There are two bodies starting with different temperatures and specific heat capacities (for simplicity assume that the bodies are solid to the volumes are constant). Let the rate of heat flow from ...
0
votes
1answer
36 views

Chemical potential in terms of temperature and pressure

For part (a), I know how to take the partial derivatives of S to get chemical potential, pressure. But there seems that I still need one equation to correctly express chemical potential in terms of ...
3
votes
2answers
132 views

Description of the heat equation with an additional term

I have the following equation: $$\frac{\partial U}{\partial t}=k\frac{\partial^2 U}{\partial x^2}-v_{0}\frac{\partial U}{\partial x}, x>0$$ with initial conditions: $$U(0,t)=0$$ $$U(x,0)=f(x)$$ ...
1
vote
1answer
46 views

Heat generated on thin disc plate in magnetic field [closed]

There are the eddy currents in thin circular copper plate thickness h and radius a, in a harmonic magnetic field which is perpendicular to plate and the effect of auto-induction is negligible. Now we ...
1
vote
3answers
282 views

Thermal physics question, final temperature of ice and water

Here is the question from my textbook: "In an insulated vessel, 250g of ice at $0^{\circ}$C is added to 600g of water at $18^{\circ}$C. What is the final temperature of the system?" The solution ...
0
votes
1answer
37 views

Thermal Physics, Specific Question [closed]

Question: The melting point of copper is 1080 degrees Celsius and its heat of fusion is 200 kJ/kg. If a copper coin at this temperature is completely melted by the absorption of 2000 J of heat, what ...
1
vote
0answers
41 views

Given partial derivatives find the state function

I have to find the state function of a gas (which under very low pressures behaves as an ideal gas). So, first I tried writing it as part of an equation $ dV = \dfrac{\partial V}{\partial T}\ dT + ...
0
votes
2answers
73 views

What is $k$ in Newtons Law of Cooling? [duplicate]

I am writing the definition of quantities for Newton's Law of Cooling and am not sure what to actually call k$,$ or its units. This is what I have so far $$\frac{dT}{dt}=-k(T-T_s)$$ Where ...
-2
votes
1answer
24 views

Rate of radiation of infra-red ray from a hot body?

I have the equation $\frac{dE}{dt}=a(\tau^4-\tau_s^4)$ however I can't find anywhere what E is supposed to be. It is not pointed out anywhere in the text and what is confusing is that in engineering E ...
0
votes
1answer
179 views

What does 1/k represent regarding Newtons Law of Cooling?

What does 1/k represent regarding Newtons Law of Cooling? I know k represents the cooling constant. I think the inverse of k is the time taken for the liquid to cool from its maximum temperture to ...
0
votes
0answers
11 views

Does transverse flow always assist in mixed convection?

I am dealing with both natural convection and transverse forced convection over a flat plate. There are 4 different situations: Upward-facing cold plate Downward facing cold plate Upward facing hot ...
0
votes
1answer
70 views

Using Jacobians to prove an identity

I have to prove the identity $$ \left(\frac{\partial U}{\partial V}\right)_T=T\left(\frac{\partial p}{\partial T}\right)_V-p $$ I know how to do this using Maxwell's relations, but the assignment ...
0
votes
2answers
115 views

Isobaric expansion work, W = p(V2-V1) [closed]

Isobaric process, so $W = p\Delta V$ according to my book. We have 10 kg of saturated steam at $x = 0.9$, P = 200 kPa. We add work at a rate of $700 W$ and we're interested in the time it takes. We ...
0
votes
1answer
48 views

Thermal resistance of thermal interface materials?

Thermal conductivity are often used for surfaces between the computer chip and the heat sink to increase heat transfer and they want high thermal conductivity to decrease the thermal resistance. By ...
2
votes
1answer
187 views

Formula for molar specific heat capacity in polytropic process

I found this formula for a polytropic process, defined by $PV^n = {\rm constant}$, in a book: $$C = \frac R{\gamma-1} + \frac R{1-n} $$ where $C$ is molar specific heat and $\gamma$ is adiabatic ...
-1
votes
1answer
86 views

Boundary conditions for the heat equation when solving a mass density gradient

I'm working with a mass density gradient with length $L$ and I'm trying to solve the heat equation in 1-D (mass diffusion equation, $\partial_t\rho(t,x)=D\Delta\rho(t,x)$), but I'm not sure which ...
1
vote
1answer
31 views

fusing two air containers with fixed pressures $p_1,p_2$ and temperatures $T_1, T_2$, what end-result $T$ and $p$ will be?

Let's say that I have two boxes with both volumes equal $V$, filled with an air. Air in first box have pressure $p_1$ and temperature $T_1$, likewise air in second box have pressure $p_2$ and ...
0
votes
1answer
119 views

Latent heat of vaporization

The molecular weight of water is 18.015 gram. The number of moles of water in one liter (1000 gram) will be: $3.34\times 10^{25}$ molecules (in 1kg). We know that latent heat of vaporization of water ...
3
votes
1answer
82 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 ...
0
votes
0answers
30 views

Question regarding temperature as a property of a system

This is probably silly question but I got stuck while reading “Lectures on Theoretical Physics-Thermodynamics and Statistical Mechanics” by Sommerfeld. In the first chapter it says : Temperature ...
0
votes
0answers
50 views

Thermodynamics First Law Question - Expansions

Two thermally iso- lated cylinders, A and B, of equal volume, both equipped with pistons, are connected by a valve. Initially A has its piston fully withdrawn and contains a monatomic gas at ...
0
votes
0answers
40 views

Adiabatic Expansion with expanding control volume

I have a tube with a length "L" and diameter "d" that is open on 1 side . At a certain point ( say "x" ) from the closed end of the tube, I have a gas with a high pressure. At this point, "x", there ...
0
votes
1answer
38 views

Ideal gas system with diathermic piston externally manipulated

I wanted to ask about the following problem: An ideal monatomic gas is separated into two volumes $V_{1}$ and $V_{2}$ through a diathermic piston, such that each volume containing $N$ atoms and the ...
0
votes
1answer
62 views

Comparing unknown temperature scales [closed]

Source: Principles of Physics by Resnick, Halliday, Walker. $9^{th}$ edition. Chapter 18. Problem 6. On a linear $X$ temperature scale, water freezes at $-125.0^0X$ and boils at $360.0^0X$. On a ...
6
votes
1answer
114 views

Doubts about the ideal gas law

EDITED AND SOLUTION: In fact my stupid mistake was to take the wrong value for my $P_1$ and I was getting an 1.2998 that finally is a 1,9178 within just a difference about 7%. So at the end they are ...
0
votes
0answers
87 views

Determine pipe outlet temperature without length?

Let's say I am flowing a fluid through a pipe that has a constant surface temperature. Is it possible to determine the heat flux on the inner surface without knowing the pipe's length when the only ...
2
votes
2answers
86 views

Container divided in two parts with ideal gas

I wanted to ask your help with the following problem: Consider a closed container, that is, with insulated walls impervious, and rigid. The container is divided into two parts by a wall having the ...
0
votes
0answers
27 views

where i can find thermodynamics properties of octane

where can I find thermodynamics properties for octane at $T_s$? I need this properties or where can i find all ? $$liquid-density=\rho_l=?$$ $$vapor-density=\rho_v=?$$ ...