Heat Definition and 1000 Threads

We know $$ K(x,t) = \frac{1}{\sqrt{4\pi t}}\exp(-\frac{x^2}{4t}) $$ is a solution to the heat equation: $$ \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} $$ I would like to ask how to prove: $$ u(x,t) = \int_{-\infty}^{\infty} K(x-y,t)f(y)dy $$ is also the solution to...

By using the given relationship that S=a/T --(1) along with the equation ∫ (delta Q rev)/T=∫dS -- (2) I found out that my answer for the value of Q is mc*ln (T2/T1)*a upon equating (1) & (2). But the solution is instead given as Q=a*ln*(T1/T2). I would be grateful if someone would point out...

We know heat is the motion of molecules of a gas for example. As temperature increases this motion increases and the gas expands. We know this gas would be hot if we touch it. So I want to ask how does the fast motion of molecules somehow translates to the heat that we feel. Why does it feel...

According to the Vaporization Heat table, the heat needed for 1 mol of H2O to evaporate at 100°C is 40.7KJ and 44.0KJ/mol is needed to evaporate H2O at 25°C. Thus 44.0-40.7=3.7KJ is the energy needed to heat H2O to 100°C from 25°C. However, according to the heat capacity of H2O, 3.7KJ will only...

I'm looking for a way to keep a liquid under 50°C. This liquid has a thermal conductivity of .1396 and a specific heat of 2.054 both at 40°C. and a constant energy source submerged in it ranging from 16KW to 17.5KW. I'm barely starting to read about this topic, according some forums, a car...

Hi Everyone, I am looking to find how much heat can be stored in a concrete pipe of roughly 0.3-0.4m diameter, and an internal diameter of 0.05m. Air will travel through the internal diameter at 500°C and 17.5bar which will provide the heat for the pipes. This system will then be reversed so...

i found current to be 2/5 A. then 2/5A multipled by 6s = 2.4C. and since one joule per coulomb is equal to the unit of p.d, i get 2.4J. I don't get 4.8J(supposed answer)

Summary:: How to calculate the rate of heat transfer between hot external water and cold internal water in a pipe. The image attached is my attempt at the question however, I find myself stuck trying to work out internal and external heat transfer coefficient.

I thought it might me a ratio of the atomic masses. 27 / 63.6 = x / 900 x = 382 J/kg-K

Is Mean Temp in 2 phase Heat Exchangers Higher Than Logarithmic Mean? I am looking at this paper: https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1314&context=iracc Having a bit of trouble understanding all of it, but my basic question is just: If I have a heat pump where the hot...

Summary:: Heat capacity for real gas with ideal gas (zero pressure) equation I'm looking at this problem and I'm stuck. I usually question everything but this problem is confusing me. I don't know how they've made the jump from reduced properties (from generalized Cp charts(?)) to...

I want to solve the heat equation numerically. The equation is: $$k \dfrac{\partial^2 T}{\partial x^2} = \dfrac{\partial T}{\partial t}.$$ This is a parabolic PDE. Following this pdf (specifically, equation 7 given on page 3), I wrote the following Python function to implement the explicit...

@Dale : “The COP of a heat pump and the efficiency of a heat engine both depend strongly on the temperatures of the hot and cold reservoirs. For this calculation you need to go back and check the sources for the temperatures corresponding to each of these numbers. You will find that the Stirling...

I was reading about heat pumps and it made me wonder… would the following process be physically possible…? I attach the hot side of the heat pump to the hot side of the stirling engine. 400% COP (coefficient of performance) means 1 kilowatt hour of electricity consumed by the heat pump delivers...

I have a simple question sort of about exact differentials and deciding which variables matter and when. I know we can write entropy ##S## as ##S(P,T)## and ##S(V,T)## to derive different relations between heat capacities ##C_V## and ##C_P##. I was wondering if it is technically correct to...

ΔQ=mC(T3-T1) But, will this C be Cp or Cv. Both pressure and volume changes. So, neither of them can be. Feeling so confused

Hi, i have this question and don't understand it. can somebody explain what i have to do. i know a ideal engine is a engine running on carnot cycle i what the cycles are i don't know what relative efficiency is and what there looking for (Q) Review the relative efficiency of ideal heat engines...

I've been given the following 2 questions (please see below), and I've been asked to come with answers and arguments for my decision for the proposed answer, since there is just 1 correct answer per question. (so you can see my attempt below) Q1)The refrigerants have to: a)Vapourise at high...

Hey guys! This is problem from Callens Thermodynamics textbook and I'm stuck with it. My goal was to get a expression for the entropy ##S## which is dependent on ##T## so I can move into the ##T-S##-plane to do my calculations: I startet by expressing the fundamental equation as a function of...

A steel pipe with foam insulation is embedded in a concrete wall. The steel pipe is carrying cold water and therefore gains heat from outside atmosphere. Heat transfers through the concrete wall, foam insulation and then to the pipe. Is it possible to calculate critical radius of insulation for...

By definition ##C = T_H \dfrac{\partial S}{\partial T_H} \bigg{)}_Q## so given ##A=4S## we first need to work out the area of the event horizon. More specifically, let ##\Sigma## be a partial Cauchy surface of constant ##v## in ingoing EF ##(v,r,\theta, \phi)## co-ordinates then ##A## is the...

My experiment procedure is that I am using burning charcoal as the heat source, and there are three thermocouples used, first one measuring the temperature of the charcoal, second one measuring the inner temperature of the concrete block, third thermocouple is placed on the top part which is...

So firstly, I don't understand if the mass flow rate is for steam or for water. If it is for water, I know I can find the heat transfer rate using equation:Q=mcdeltaT. But then I don't know how to find h (the average heat transfer coefficient) because I don't know the surface area (As). I can...

Hi, I am trying to understand how I can estimate the time it takes for a fluid at room temperature flowing through a thin capillary glass tube (2 mm ID) connected to an oven to reach the equilibrium temperature (oven temperature). Assuming the oven is preheated and the tube inside the oven is...

answer is 78oCdelta G = delta H - T delta S -235,310- (-277,690) = -38.56e3- T (282.59-160.70) T = -664K I am not sure if my concept is correct. May anyone help a little bit on that please? thank you

Im practicing the questions in the problem book and seem to be getting different answers to the book can somebody check cheers. [Answers: 57.99 W/m: 1739.7 W: 84.9ºC] textbook answers A water pipe of bore 65 mm bore and 6mm wall thickness, carrying water at 85ºC is insulated with one layer of...

Homework Statement:: why does heat capacity depend on the mass/size of the object when it's units is J/K , and why is specific heat capacity dependent on the material/substance when it's unit is J/kgK? Relevant Equations:: Q=Cθ Q=mcθ -

the answer is 1/2 , but when I did the working out, I got 2/1.. so I'm quite confused

I remember when I was in high school, heat was very often said to be a factor of speeding up chemical reactions that we all know, because heat is actually energy, energy will excite the molecules and make them easier to collide with other molecules or leave its own molecules (breaking bond)...

Hey guys! I'm currently struggling with a specific thermodynamics problem. I'm given the entropy of a system (where ##A## is a constant with fitting physical units): $$S(U,V,N)=A(UVN)^{1/3}$$I'm asked to calculate the specific heat capacity at constant pressure ##C_p## and at constant volume...

This has persistently bugged me in my intro plasma course. They keep using ##\gamma = 3## aka ##N_d = 1## (where ##N_d## is the number of degrees of freedom in the molecule) as an approximation. See for example, the Bohm-Gross dispersion curve. I can tell you from deriving this that the factor...

Can anyone help me with this? -How much heat must be added to 3.5 m3 /s of moist air with a dry bulb temperature of 10°C and a relative humidity of 60% to raise the temperature of the air by 17°C? • What will be the relative humidity of the air once this heat is added? • What is the power...

Can anyone help me with this? -How much heat must be added to 3.5 m3 /s of moist air with a dry bulb temperature of 10°C and a relative humidity of 60% to raise the temperature of the air by 17°C? • What will be the relative humidity of the air once this heat is added? • What is the power...

On the surface of a semi-infinite solid, a point heat source releases a power ##q##; apart from this, the surface of the solid is adiabatic. The heat melts the solid so that a molten pool forms and grows. Let's hypothesize that the pool temperature is homogeneously equal to the melting...

Well, internal energy is the sum of the kinetic and potential energies of all the molecules within a given mass of a substance; this energy is associated with the random, disordered motion of the molecules. An example of internal energy is compressed gases; since gases occupy the total volume...

Yes, heat can flow into a body without increasing the mean kinetic energy of its molecules. Transferring heat energy to an object will raise its internal energy, this will not necessarily cause an increase in temperture. Specific latent heat is the energy required to change the state of one...

The heat pump comprises of the 4 components: evaporator, compressor, condenser and expansion valve. Thermal power required to heat the building: 12.1 kW at condensing temperature tc = 44.3 deg C For the evaporator: vaporizing temperature tv = -7 deg C Subcooling temperature for the heat pump Δ...

I spent hours looking at this and cannot figure out where the error is. I'm wondering if there is an error before the boxed expression. @Orodruin and @PeroK may I ask for your assistance?Consider a solution ##u:[0,\infty)\times \mathbb{R}^n\rightarrow \mathbb{R}## of the heat equation, ie...

The answer is 6470 J. So since I have the two temperatures I could calculate the efficiency. First I convert to kelvin then get an efficiency of 0.35481. Now I can use e=W/Qin to get Qin. I get a value of 10033.54J. Now I can use e=(Qin-Qout)/Qout to get Qout, the waste heat. I get 7405.9 J...

(3) To solve the initial value problem $$\begin{cases} \partial_t\phi-\partial^2_x\phi=0 & \text{in}\quad (0,\infty)\times R \\ \phi(0,\cdot)=\psi & \text{on}\quad \{t=0\}\times R \end{cases}$$ we use the fundamental solution in 1D $$\Phi_1(t,x)=\frac{1}{\sqrt{4\pi...

So efficiency is W/Qin. W= 0 for isochoric processes and for the isobaric, P(change in V). So W=Pi(Vi-Vf)+Pf(Vi-Vf) Qin is negative Qs.This would happen at step 2 and 3. For the isobaric, Q=ncv(change in T) and for isochoric, Q=ncp(change in T). Now if I put everything in the equation I get...

My attic gets very hot even with the exhaust fan I installed. I would like to move than heat to my swimming pool. I currently have a FAFCO solar pool heater where the pool pump pumps water up onto my roof and thru the 12' long solar panel and down back into the pool. I would like to free up roof...

a) Ew = EL + Ei mwc(T2-T1) = miL + mic(T2-0) 160 x 4.2 x (30 - 20) = 20L + (20 x 4.2 x 20) L = (6720 - 1680)/20 = 252 J/g b) accounting for 3 gram of melted ice 160 x 4.2 x (30 - 20) = (20 - 3) + (20 x 4.2 x 20)...

I have solved the first 2 parts. For the 3rd part, I have obtained the equation: T(x) - T0 = (T1 - T0)e^(-Φx/fc), where f = fm in the question. How do I obtain that expression for H? Thank you!

So first I found rate of heat change using the above equation, with T=883K, e=1, SA= 6*l^2=21.66 Now dQ/dt=746593.71 W Now I am not sure entirely what to do next. They give density so I likely have to get the mass from that, M=pV,=1.9^3*4037=27689.783 kg. My issue is that I don't know how to...

I've come to a grinding halt with this and I can't see a way forward. Can someone please take a look at what I've done so far and let me know if what I have done is OK and then if it is, give me a hint on how to proceed. First up, Is ## u \cdot \nabla \cdot T = u_\alpha...

I'm trying to complete this past exam paper Q. Water volume = 200hl = 20000L 1L=10^-3 m^3 20000L = 200 m^3 Density of water at 15 deg C = 999 kg m^3 Density = Mass/Volume 999 kg m^3 = Mass/(200 m^3) Mass of water = (200)(999) = 199800 kg Heat required to to heat 199800 kg water: Q =m C dT =...

This is from Evans page 50. I'm sure it's something simple, but I don't follow the change from $$ \frac{\partial}{\partial t} \quad \text{to} \quad -\frac{\partial}{\partial s}$$ and from $$ \Delta_x \quad \text{to} \quad \Delta_y$$. \begin{gather*} \begin{split} u_t(x,t) - \Delta u(x,t) & =...

In answering questions (a.) Why heat intake in this system is ## \Delta Q_{sys} = ( \Delta Q_{hot water} + \Delta Q_{cold water} ) / 2 ## where. ##\Delta Q_{hot water} = c(T_1 - T_f) ## ##\Delta Q_{cold water} = c(T_2 - T_f) ## I think T or T_f should be between T_1 and T_2 But why is the...

The balanced reaction wil be : ##2C_6H_{6(l)}+15O_{2(g)}->12CO_{2(g)}+6H_2O_(l)## in order to compute the the standard enthalpy of reaction : ##\Delta H°_{f} H_2O_(l)= -285,8 \frac {KJ}{mol}##; ##\Delta H°_{f} CO_{2(g)}= -393,5 \frac {KJ}{mol}##; ##\Delta H°_{f} C_6H_{6(l)}=49,04 \frac...