What is Heat capacity: Definition and 437 Discussions

Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K).
Heat capacity is an extensive property. The corresponding intensive property is the specific heat capacity, found by dividing the heat capacity of an object by its mass. Dividing the heat capacity by the amount of substance in moles yields its molar heat capacity. The volumetric heat capacity measures the heat capacity per volume. In architecture and civil engineering, the heat capacity of a building is often referred to as its thermal mass .

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  1. A

    Specific heat capacity, Q = mcθ

    Homework Statement Here is the original question (just read the English version). Homework Equations Q = mcθ Specific heat capacity of water, c = 4200 J/kg °C The Attempt at a Solution I did Q_(absorbed) = Q_(released) mcθ = mcθ mθ = mθ And I solved for the final temperature, which is...
  2. patrickmoloney

    Relation between heat capacities and van der Waals equation

    Homework Statement Find the expression for c_p - c_v for a van-der-waals gas, with the equation of state \Bigg{(}p+\dfrac{a}{V^2}\Bigg{)}(V-b)=RT Homework EquationsThe Attempt at a Solution Basically I've proved c_p - c_v = \Bigg{[} p + \Bigg{(}\dfrac{\partial E}{\partial V}\Bigg{)}_T...
  3. J

    Heat capacity of a heating element, in a flow of air

    Air is flowing through a pipe, through a heater matrix. Flow, Inlet temperature and heater power vary. Is it possible to calculate the heat capacity of the matrix by using the Inlet & outlet temperatures, power & flow? I'm assuming no heat loss to the pipe walls to make it easier, but I'm not...
  4. D

    Specified equation of state from heat capacity

    Homework Statement The constant-volume heat capacity of a particular simple system is c_v = AT^3 where A is a constant. In addition the equation of state is known to be of the form (v-v_0)p = B(T) where B(T) is an unspecified function of T. Evaluate the permissible functional form of B(T)...
  5. C

    Is specific heat capacity always ignored in Steady State

    Hi, I want to simulate a forced convection cooling problem. Air at ambient temperature is forced through a fan into a system to cool electronics and I would like to assess the temperature of the outlet air. Actually I'm interested in the delta between the ambient and outlet temperature. This...
  6. A

    Negative heat capacity and thermal reservoir

    Say you have an object with a negative heat capacity. This means that the object increases in temperature as it radiates energy and decreases in temperature as it absorbs energy. I don't understand why this object cannot be in thermal equilbrium with a reservoir. Any help would be greatly...
  7. S

    Heat capacity at constant volume and density

    Hello! I encountered in a problem the terms heat capacity at constant volume and density (##n##) and heat capacity at constant chemical potential (##\mu##) and volume and I need to prove a relation between them. What is their definition? I thought that for the first one it would be...
  8. Rizwan Yaseen

    Heat capacity equation units

    How we change the units of Heat capacity equation to British engineering system Cp=2. 657*10^4 +42. 37T - 1. 425*10^-2T^2
  9. Carlos

    Heat capacity as a function of T under 298 K for metals

    The heat capacity equation Cp for copper as a function of temperature (Shomate equation) for the solid phase is defined for the range of 298-1358 K in the Nist Webbook and in many books. http://webbook.nist.gov/cgi/inchi?ID=C7440508&Mask=2#Thermo-Condensed And I need to calculate the heat...
  10. V

    How to apply the First Law of Thermodynamics to this problem?

    Homework Statement A spring (k = 500 N/m) supports a 400 g mass which is immersed in 900 g of water. The specific heat of the mass is 450 J/kg and of water is 4184 J/kg. The spring is now stretched 15 cm and, after thermal equilibrium is reached, the mass is released so it vibrates up and...
  11. N

    Molar heat capacity at constant pressure/volume

    Morning I am being stupid but cannot work out these problems: 1. Energy supplied to 2.0 moles of an ideal gas is 117J and it changes the temperature by 2.0K (at constant pressure).2. Calculate both molar heat capacities at constant P and V.3. Firstly, I divided 117J by 4 to get the energy...
  12. gsyz

    How can heat capacity be determined when both pressure and volume are changing?

    Hello all, I am taking a thermodynamics course and unfortunately my professor is not very instructive. I have attended every class and I still feel lost. I was wondering how it is possible to find heat capacity if both the pressure and the volume are changing? I was under the impression that...
  13. pangru

    I Why does the heat capacity of solids drop exponentially at low temperatures?

    According to Einstein (or Debay) model of solids, heat capacity drops exponentially at low temperatures: question is >> why it changes so dramatically at low temperature that is physical explanation of this?
  14. B

    [PoM] Rotational and vibrational heat capacity

    Hi guis, i need your help... 1. Homework Statement Evaluate the rotational and vibrational contributions to the heat capacity of a gas of DBr (D=deuterium, Br=mixture at 50% of 79Br and 81Br) at 380 K temperature, knowing that the bond distance is 1.41 Å and the vibration frequency of 1H79Br...
  15. binbagsss

    Plot Heat Capacity vs Temperature for a 2 state system microcananonical ensemble

    Homework Statement I have ##C= NK_B (\frac{\epsilon}{K_B T})^{2}e^{\frac{\epsilon}{K_B T}}\frac{1}{(e^{\frac{\epsilon}{K_BT}}+1)^2} ## and need to sketch ##C## vs. ##T## Homework Equations See above The Attempt at a Solution I have ##C= NK_B (\frac{\epsilon}{K_B...
  16. Adrianus

    What heat capacity is needed to evaporate water in oil

    Homework Statement In an industrial fryer is f.e. 400 kW. Heating capacity installed. The fryer may contain as much as 1.450 ltr of oil. I can fry 2.000 kg of chicken nuggets per hour in that. These products loose 7% of moisture/water in this process. That water can only escape from oil in gas...
  17. T

    Thermal Physics (Specific Heat Capacity)

    Homework Statement Body X whose temperature is 0 °C is brought into thermal contact with body Y of equal mass and temperature 100 °C. The only exchanges of heat that take place are between X and Y. The specific heat capacity of X is greater than that of Y. Which statement about the final...
  18. VegemiteJuice

    Determining the specific heat capacity of water

    Homework Statement Hi, I have an assignment to determine the specific heat capacity of water using a calorimeter, voltmeter and ammeter, where we connected the calorimeter to a 10V power pack and measured the temp of the water and the readings on the voltmeter and ammeter every minute. I ended...
  19. arpon

    Temperature dependence of Cv at very large volume

    Homework Statement In the case of a gas obeying the equation of state $$\begin{align}\frac{Pv}{RT}&=1+\frac{B}{v}\end{align} $$ where ##B## is a function of ##T## only, show that, $$\begin{align}c_v&=-\frac{RT}{v}\frac{d^2}{dT^2} (BT)+\left(c_v\right)_0\end{align}$$ where ##\left(c_v\right)_0##...
  20. S

    Heat Capacity and Latent Heat question

    Homework Statement A 75.0g ice cube at 0 C is placed in 825g of water at 25 C. Find final temp. Homework Equations Well none really, this should be simple plugging into to heat equations. The Attempt at a Solution Heat required to melt ice = (0.075kg)(3.33*10^5) = 24975 J Heat required to...
  21. RabbitWho

    Find the mass of a metal block with heat capacity 60JK

    Homework Statement A metal block of heat capacity 60 J K -1 loses 1MJ of heat energy to its surroundings. Find the decrease in its temperature. Homework Equations Q = m c Δ θ Heat energy added = mass x specific heat capacity x rise in temperature heat energy lost = blah blah blah x drop in...
  22. J

    Heat capacity under constant pressure or volume question

    HOMEWORK POSTED IN WRONG FORUM, SO NO TEMPLATE I have encountered a problem at the university in which there is a thermally isolated container of constant volume in which the number of particles and temperature change with time(the temperature increases). The change in particle number ensures...
  23. K

    Calculating molar heat capacity from electron contribution

    Homework Statement Silver has a Fermi energy of 5.48 eV. Calculate the electron contribution to the molar heat capacity at constant volume, Cv, of Silver at 300 K. Express your result as a multiple of R. Is the value of Cv due principally to the electrons? If not, to what is it due? ans...
  24. J

    Specific heat capacity and concentration

    Hello. I am doing a research paper on the relationship of specific heat capacity and refractive index of liquids. I am doing this by finding the relationship between specific heat capacity and concentration and refractive index and concentration. With this I can find a general trend and conclude...
  25. T

    Calculating combustion temperature of mixture

    Hey guys, I'm trying to write a small article that very simply explains some of the math involved with a rocket engine. I'm not looking for a very accurate answer so I tried the following method 1) Stoichiometry on the fuel which was sugar and saltpeter and their respective enthalpies of...
  26. timelesstrix0

    Specific heat capacity of a mixture

    so for one of my assignments i need to make a calculation which involves the mixture to be made of different types of substance... the heat capacity for each of the different unknown substances that were given: substance 1 = 1250J/kg °C substance 2 = 1130J/kg °C substance 3= 4100J/kg °C i need...
  27. S

    Thermodynamics and heat capacity

    Homework Statement A 10.0 g sample of solid platinum is placed in a large, sealed vessel at a sufficiently low pressure that the platinum is able to sublimate directly to a gas. Some thermodynamic properties of platinum at low pressure are given in the following table. Molar mass, M - 195...
  28. adriplay

    Heat capacity in gas simulation

    I have a simulation with a bunch of particles with volume bouncing around in a box with no interaction between them, a hard-sphere gas. Initially, they all have the same momentum |p|=√(2⋅m⋅2/3⋅k⋅T) to have the average kinetic energy 3/2⋅k⋅T. I'm asked to add a constant energy flux to the system...
  29. L

    Which Container is Hotter After 30s? Exploring Heat Transfer

    Homework Statement In each of the following, state and explain which container will have the hotter liquid after thirty seconds: a) You pour equal amounts of of hot coffee into two cup s from a percolator. The cups are the same general size and shape. One is made from heavy china one is made...
  30. M

    Heat capacity at constant volume and internal energy

    I am wondering if equation $$C_v=(\frac{∂U}{∂V})_T$$ applies only to ideal gases or applies generally for any other system? The second question I have is can we use the following relation: $$dU=nC_vdT$$ in processes that are non isochoric (that is for processes where volume is not constant)? I...
  31. S

    Estimate vibrational frequency of N2 molecule

    Homework Statement Experimental data for the heat capacity of N2 as a function of temperature are provided. Estimate the frequency of vibration of the N2 molecule. Homework Equations Energy of harmonic oscillator = (n+1/2)ħω C=7/2kB Average molecular energy = C*T But this is an expression...
  32. Alfreds9

    Water evaporation, temperature, wind and heat capacity?

    Hi, I'd like to know how I'd put together, either elegantly or at least in physical terms, that surely water evaporation in a large pool of V volume and S surface is influenced by wind (increased by it as opposed to having side barriers), temperature (increased by direct sunlight as opposed to...
  33. B

    Heat Capacity of Distinguishable Particles

    Homework Statement A system of N distinguishable particles, each with two energy levels. The lower energy level has energy equal to zero, and the higher energy level has energy ##\epsilon##. The higher energy level is four fold degenerate. Calculate the heat capacity. Homework EquationsThe...
  34. S

    What are the heat capacity values of diesel in liquid and vapor states?

    What is the heat capacity values of diesel in liquid and vapour state?
  35. Y

    Specific Heat Capacity Graph Question

    Homework Statement My answer is question 3 part c the graph. SHC = c http://www.ocr.org.uk/Images/61757-question-paper-unit-g484-the-Newtonian-world.pdf [See page 7]Homework Equations E=mcdelta theta Power=Energy/Time Therfroe Power*Time = Mass*c*delta theta. The Attempt at a Solution See in...
  36. M

    How many kg of ice must be dropped to make Tf= 22.7C?

    Homework Statement An insulated beaker with neglible mass contains .3kg of water at a temp of 78.6 C. How many kg of ice at -19.6 C must be dropped into the water to make Tf= 22.7C? Specific heat for water= 4190 J/kgK specific heat for ice= 2100 J/kgK heat of fusion for water= 334kJ/kg...
  37. M

    Thermodynamics, use of Cv and Cp

    I am studying for a thermo exam, and one of the problems I am doing deals with adiabatic expansion of a piston in a cylinder. When solving for work, the solution guide uses m*Cv*(T2-T1). I don't understand why they know how to use Cv instead of Cp. The pressure changes, so obviously you wouldn't...
  38. E

    Specific heat capacity of a metal at low temperature

    Homework Statement The specific heat capacity of a metal at low temperature (T) is given as ##C_p = 32\left({\dfrac{T}{400}}\right)^3## (kJK-1kg-1). A 100g vessel of this metal is to be cooled from 20 K to 4 K by a special refrigerator operating at room temperature (27°C). The amount of work...
  39. S

    Is Dropping a Metal Block into a Lake a Reversible Process in Thermodynamics?

    Hello all. I have a quick question about entropy... I've just been formally introduced to it. Consider the example of a metal block of mass m and heat capacity Cp at temperature T1 = 60C being dropped into a large lake of temperature T2 = 10C. $$\Delta S_{block} =...
  40. F

    What is meant by heat capacity at constant pressure?

    Generally in chemistry and physics, we learned that a material has a heat capacity at constant pressure. However, I am confused at whether this refers to a constant external pressure or a constant system internal pressure? Thanks.
  41. Marcin H

    Oxidation and specific heat capacity

    Homework Statement If a metal is highly susceptible to oxidation, what effect might this have on calculating the quantity of heat transferred to a metal? Use specific examples. Homework Equations Q=mcΔT The Attempt at a Solution Would oxidation change the specific heat of the metal? Since...
  42. Reety

    Why do lower temperatures result in lower specific heat capacity?

    Equations: E=m*c* dTheta or T Experiment: I had two beakers of water with one thermometer in each beaker. One beaker had boiling water and the other beaker had room temperature water. I also had a 100g mass. I recorded T1 which was the intial temperature of the cold water. I then put the mass...
  43. Coffee_

    Finding the entropy from the heat capacity

    Let's say that we have some canonical ensemble where I know that the heat capacity is given by ##C_{V}=\alpha(N,V) T^{n}## Since ##C_{V}=T\frac{\partial S(T,V)}{\partial T}## I know that ##S(V,T)=\frac{1}{n} \alpha(N,V) T^{n} + f(N,V) ## Where the function ##f(N,V)## has to do with the fact...
  44. P

    Correct mathematical notation for Volumetric Heat Capacity

    What is the correct notation for Volumetric Heat Capacity? I see it written both ways (Wiki for example). I'm pretty sure one is more correct but which is it? (1) Btu/ft³·°F or (2) Btu/(ft³·°F)
  45. M

    Specific Heat Capacity for Gas

    So I have a question regarding the specific heat capacities in thermodynamics. In general the specific heat capacities for a gas (or gas mixture in thermo-chemical equilibrium) can be expressed as, ## c_p = \left(\frac{\partial h}{\partial T}\right)_p \qquad \text{and} \qquad c_v=...
  46. T

    How to find the specific heat capacity of a mixture?

    Homework Statement For my physics IA, I am finding the specific heat capacity of water-solute mixtures and finding how the specific heat differs from that of just water alone. I have the mass of the mixture, for example baking soda and water was 914.75g and changed 175.8 degrees Fahrenheit in...
  47. M

    What is the relationship between heat capacity and temperature?

    Hello, I'm reposting this 'cause I think it's more relevant here than where it was posted before. Not sure how to delete the other one... I'm trying to plot the heat capacity as a function of the temperature from some small temperature to Debye's using numerical summation over the energy (shown...
  48. J

    How do you calculate total heat capacity for a house/wall?

    I was wondering how I might be able to calculate the total heat capacity for a house given the individual heat capacities of the components. For example, if I take a given wall and break it down into its components for a lumped parameter model, I'll have some thermal capacitances in in...
  49. Andrei316

    (0.04)c(33.7-23.5)+(0.08)c(33.7-39.6) Find C

    Sorry if the title is against the rules or anything, I just wanted to be specific as possible :P 1. Homework Statement V1(Saltwater) = 40g = 0.04kg V2(Hot-Saltwater) = 80g = 0.08kg Ti(Saltwater) = 23.5oc Ti(Hot-Saltwater) = 39.6oc Tf = 33.7c Question: A cup of 40g saltwater is at 23.5c & A...
  50. rthrbe

    Specific heat capacity of water

    I had an experiment to find the specific heat capacity of water. Materials are electric kettle, logger pro, 1 kg water, and set up the time to 240 seconds. The experiment value i got is 4.33 kJ/(kg.K) which is closed to the waters specific heat capacity 4,18 kJ/(kg.K). I wonder what could be...
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