0
votes
0answers
15 views

thermodynamics first law sign convention based problem [on hold]

Consider a (frictionless) piston-cylinder system. Initially, one mole of an ideal gas is present in the cylinder. The pressure and temperature of the gas are 1 bar and 300 K. A stirrer slowly ...
0
votes
1answer
10 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
42 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
0answers
21 views

Thermodynamics Assignment: Combustion [closed]

Acetylene, Methane and Octane are burnt in air (75% Nitrogen, 25% Oxygen) and forms Carbon Dioxide, Carbon Monoxide, Nitrogen and Water This is the unbalanced equation: C2H2 + CH4 + C8H18 + O2 + N2 ...
-1
votes
1answer
38 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
25 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
36 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
74 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
28 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
36 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
31 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
27 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
45 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
105 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
34 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
64 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
25 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
16 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
56 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
68 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
36 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
65 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
51 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 ...
0
votes
1answer
27 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 ...
2
votes
1answer
43 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
46 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
49 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
120 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
59 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) = ...
0
votes
0answers
68 views

Caculating thermal stresses in a composite rod

The Question Between two rigid walls separated by a distance $l_1+l_2$, two rods of equal cross-section area $A$, and length, coefficient of linear expansion and Young's modulus $l_1, ...
1
vote
0answers
32 views

Maximum temperature of an elliptical thermodynamic process

Given a heat engine made from the curve $$V(t)=V_0 +A \cos(\omega t); \qquad P(t)=P_0-B \sin(\omega t).$$ What are the hottest and coldest points of this cycle, and what are the temperatures at those ...
1
vote
0answers
137 views

Basic Thermodynamics: Quasistatic Adiabatic Process

I'm going through the exercises in a Thermodynamics book, just to revise and build my intuition. Right now, I'm working on: Show that for a quasistatic adiabatic process in a perfect gas, with ...
1
vote
1answer
61 views

Relation between speed of sound and compressibility

We know that $c^2=\frac{\partial p}{\partial ρ}$ The adiabatic compressibility is defined as: $\beta_S=-\frac{1}{V}\frac{\partial V}{\partial p}$ such that the subscript "S" stands for "adiabatic" ...
0
votes
0answers
63 views

How to do Legendre transformations on a S=S(U,V) P,V,T system?

Problem: For a $P,V,T$ system with constant mass,entropy can be considered a function of $U,V$, i.e. $S=S(U,V)$. The goal is to derive the rest of the thermodynamic functions via Legendre ...
0
votes
1answer
92 views

Which one conducts heat better: water, or air?

If we were to assume room temperature of 20C, which of the fluids conducts heat better, and why?
0
votes
0answers
86 views

Find state equation given cubic expansion and isothermal compressibility coefficients

Context: I'm studying basic thermodynamics. Since I'm not confident that I translate the terms correctly, let me define the following coefficients mathematically: \begin{equation} \beta = ...
3
votes
0answers
89 views

Why is Clapeyron equation so important?

Context: I'm studying basic thermodynamics. My textbook has a chapter on the Clapeyron equation which, as a reminder, is given by the following formula: \begin{equation} \frac{dP}{dT} = \frac{\Delta ...
0
votes
0answers
27 views

Transient conduction - Biot number with irradiation?

I understand that the Biot number is essentially the ratio of the convective effects to the conductive effects in transient conduction but what if there is some sort of radiation from a heat source ...
0
votes
0answers
16 views

Work of an adiabatic/ compresion: sign?

As far as I am concerned the adiabatic work it is given by: $$ W_{adi}=\frac{P_{f}V_{f}-P_{i}V_{i}}{\gamma -1}$$ While I have seen in other examples that it is used with $1-\gamma$ in the ...
0
votes
1answer
64 views

Trying to turn a nonlinear differential equation into a linear one

The problem I have today is to determine the differential equation for a square fin protruding from a wall that experiences surface to ambient radiation and has an internal heat generation of $\dot q$ ...
5
votes
2answers
130 views

Thermal equilibrium in general relativity

The Newtonian condition for thermal equilibrium for a static system is $T = \mathrm{const}$. In this homework I'm asked to show that it's curved space generalization is $T(-g_{00})^{\frac{1}{2}} = ...
1
vote
0answers
72 views

How much heat needed to heat 400g of ice at 0°C to 20°C in a 200g aluminium pot? [closed]

An aluminium pot has a mass of 200g and contains 400g of ice at 0°C. How much heat would be needed to melt that ice and then raise the temperature of the resulting water to 20°C. The specific heat ...
2
votes
1answer
97 views

How does the internal energy and entropy depend on mass?

I've found this thermodynamics question: Given a fluid described by the following equations: $$PV^{1/3}=aT^3 ,\quad U=3aT^3V^{2/3}, \quad S=\frac{9}{2}aT^2V^{2/3}$$ The parameter $a(n)$ ...
0
votes
1answer
97 views

is this heat calculation equation correct?

If I have a line of copper wire (lets say $\textrm{1 meter}$ long, $\textrm{1 mm}$ thick) and one end is a flattened disk of copper about the size of a quarter, and I apply a lot of heat to it (I'm ...
0
votes
2answers
103 views

Why does the coefficient of performance need to be calculated with $W + Q$?

How much work must a heat pump with a COP of 2.50 do in order to extract 1.00 MJ of thermal energy from the outdoors (the cold reservoir)? The first formula that came into my mind after reading ...
1
vote
0answers
133 views

Radiative cooling time for a black body

Okay, so this is confusing me a bit. How can I calculate the time it takes to cool a perfect black body from an initial temperature $T$ down to equilibrium temperature (say, 3 K for space)? I know ...
2
votes
0answers
52 views

Time needed to heat water in a pot [closed]

I have a pot with water of mass $m$ and it is heated by a stove element of temperature $T_E$ and with a surface area of $A$. The water starts at temperature $T_W > 0^\circ\, C$. How ...
0
votes
0answers
33 views

Expression of $\kappa_S$ in photon gas

I'm calculating some properties of the photon gas. That gas is defined by $$U=aVT^4$$ $$P=\dfrac{1}{3}aT^4$$ I calculated photon gas entropy: $$S = \dfrac{4}{3}aT^3V $$ I could calculate $c_V$. ...
0
votes
2answers
228 views

How do you calculate the change in temperature of an adiabatic system?

I really don't even know how to start doing this problem. I understand PV=nRT and I understand that if either T, V, or P is kept constant, then the other 2 change at the same rate, and I understand ...