-1
votes
0answers
21 views

heat supplied by two heat source in reversible heat engine [on hold]

A reversible engine is supplied with heat from two reservoirs at 900 K and 600 K and rejects heat to a sink at 300 K. The engine develops work equivalent to 90kJ/s and rejects heat at the rate of 56 ...
2
votes
1answer
40 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
37 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
46 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
24 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
60 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
63 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
56 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
72 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
20 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
35 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
128 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
45 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
234 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
36 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
40 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
70 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
21 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
166 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
10 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
68 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
101 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
45 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
149 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
79 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
30 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
104 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
80 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
47 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
38 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
37 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
56 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
113 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
73 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
81 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
26 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 ? $$liquid-density=\rho_l=?$$ $$vapor-density=\rho_v=?$$ ...
0
votes
0answers
19 views

Building a magnetron powered steamer

I am wanting to build a microwave powered steamer for a reverse engineering project in university. I've read up some on this and know that its not as efficient as a heating element. I'm curious about ...
1
vote
1answer
69 views

Fluid Temperature as a function of Mass and Ambient Temperature

Problem I am trying to create an equation to calculate fuel temperature based on ambient temperature, heat exchange rate, and mass. The idea is very simple; when the mass is heated, depending on how ...
3
votes
2answers
74 views

Prove identity of partial derivatives

I can not do the following problem: Prove the identity: $$\left( \frac{\partial x}{\partial y} \right)_{z}\left( \frac{\partial y}{\partial z} \right)_{x}\left( \frac{\partial z}{\partial x} ...
1
vote
0answers
47 views

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 ...
1
vote
0answers
93 views

Partition Function of a three state particle system

I've just finished studying the partition function of a two-state particle system, where particles can have a 0 energy value or E energy value . That is: Where $t_j$ is a variable of value ...
2
votes
0answers
68 views

Finding internal energy using equation of state

I have an equation of state as a function of $p$ (pressure), $T$ (temperature) and $V$ (volume) for a real gas and need to find an expression for the internal energy $U$. I know this is given by the ...
1
vote
1answer
46 views

Can I apply symmetry to this boundary value problem (BVP)?

Let's say I have a hollow cylindrical shell with inner radius $a$ and outer radius $b$ and length $L$. The temperature at at z=L is $T_{2}$ and the temperature at z=0 is $T_{1}$. There is also an ...
6
votes
4answers
93 views

Bulk flow of air in a long tube between Antarctica and Australia?

I have a 5km diameter clear plastic tube which is open at each end and runs from the center of Antarctica to Lake Eyre in Australia. The tube is on the ground where it can be and at sea level on the ...
1
vote
2answers
50 views

Temperature limit on entropy of a paramagnet

We have $$S=Nk_B[\ln(2 \cosh(x)) - x \tanh(x)]$$ where $$x = \frac{\mu B}{k_BT}$$ In need to show that at low temperatures entropy $$S \approx Nk_B2xe^{-2x}$$ I wrote out the $\cosh(x)$ in terms of ...
0
votes
2answers
54 views

Molecules of a solid [closed]

Question: Molecules of a solid : (a) are always in a state of motion (b) move only when heated (c) move because they are loosely bound (d) do not move at all My attempt: I ...
3
votes
2answers
124 views

Pressure versus Volume system problem

A rigid air tight container of volume 1.5 m$^3$ is filled with a gas of density 8 kg/m$^3$. The container has a density meter that allows us to watch the changes in density in the gas in the ...
0
votes
2answers
74 views

Entropy of a chain

A chain has N segments which can be oriented in either the x or y directions. For each segment oriented along y, there is an energy penalty of $\epsilon$. We also know the end segment is at $(L_x, ...
1
vote
1answer
62 views

Calculating energy U from $\partial U/\partial q$

Imagine $N$ oscillators with only two possible energies, $\epsilon_0$ and $ \epsilon_1$, with $\epsilon_1 > \epsilon_0$. Taking $\epsilon_0 = 0$ for now I showed $\Omega(q\epsilon_1) = ...