What is Specific heat: Definition and 481 Discussions

In thermodynamics, the specific heat capacity or occasionally massic heat capacity (symbol cp) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample. Informally, it is the amount of energy that must be added, in the form of heat, to one unit of mass of the substance in order to cause an increase of one unit in temperature. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules so the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.The specific heat capacity often varies with temperature, and is different for each state of matter. Liquid water has one of the highest specific heat capacities among common substances, about 4184 J⋅kg−1⋅K−1 at 20 °C; but that of ice just below 0 °C is only 2093 J⋅kg−1⋅K−1. The specific heat capacities of iron, granite, and hydrogen gas are about 449 J⋅kg−1⋅K−1, 790 J⋅kg−1⋅K−1, and 14300 J⋅kg−1⋅K−1, respectively. While the substance is undergoing a phase transition, such as melting or boiling, its specific heat capacity is technically infinite, because the heat goes into changing its state rather than raising its temperature.
The specific heat capacity of a substance, especially a gas, may be significantly higher when it is allowed to expand as it is heated (specific heat capacity at constant pressure) than when is heated in a closed vessel that prevents expansion (specific heat capacity at constant volume). These two values are usually denoted by



{\displaystyle c_{p}}



{\displaystyle c_{V}}
, respectively; their quotient







{\displaystyle \gamma =c_{p}/c_{V}}
is the heat capacity ratio.
The term specific heat may refer to the ratio between the specific heat capacities of a substance at a given temperature and of a reference substance at a reference temperature, such as water at 15 °C; much in the fashion of specific gravity.
Specific heat capacity relates to other intensive measures of heat capacity with other denominators. If the amount of substance is measured as a number of moles, one gets the molar heat capacity instead (whose SI unit is joule per kelvin per mole, J⋅mol−1⋅K−1. If the amount is taken to be the volume of the sample (as is sometimes done in engineering), one gets the volumetric heat capacity (whose SI unit is joule per kelvin per cubic meter, J⋅m−3⋅K−1).
One of the first scientists to use the concept was Joseph Black, 18th-century medical doctor and professor of Medicine at Glasgow University. He measured the specific heat capacities of many substances, using the term capacity for heat.

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  1. C

    Deriving general specific heat capacity formula

    For this, Dose anybody please know of a better way to derive the formula without having ##c = \frac{\Delta Q}{m \Delta T}## then taking the limit of both sides at ##\Delta T## approaches zero? I thought ##\Delta Q## like ##\Delta W## was not physically meaningful since by definition ##Q## is...
  2. lxhull

    Specific Heat Capacity of a metal bar placed into water

    Previously solved thermal energy gained by water as Eth= 0.15(4180)(17.6) = 11035.2 J Not sure if its relevant
  3. J

    I Calculating the specific heat capacity for the 2D Ising model

    So I'm looking at the book "Equilibrium Statistical physics" by Plischke and Bergersen. I'm doing the calculation of the specific heat of the 2D Ising model. I can't seen to quite get out the same expression as in the book - there are a coupe of minus signs that are different. I don't know if I...
  4. D

    Specific heat in for the Otto cycle

    A class project requires us to model the Otto cycle using ideal gas properties. We are not given the value for qin (specific heat in) and are told to make an intelligent approximation. My approach to this has been to find the calorific value of petrol, multiplying this by the density of petrol...
  5. JD_PM

    Finding specific heat C_p coefficients using NIST

    I am trying to find the specific heat (at constant pressure) ##C_p## coefficients linked to the JANAF model, which basically assumes that ##C_p## is a polynomic function of ##T##, for liquid nitrogen (at ##\approx## 97 K). Before doing that, I am trying to find those for water (at ##\approx##...
  6. N

    Thermal physics question: Specific heat capacity

    At first, I tried to calculate the heat energy required by doing this: I realized I should calculate heat energy separately instead of grouping glass and water together so I did this: But the answer is supposed to be 6.29 x 10^4. I don't know how to solve this. Can anyone help please? Thank you
  7. bluesteels

    Confusion about whether to use the specific heat of water or ice

    My thought process of how i do the ice melting part: (note I just ignore the copper/lead part cause I already know how to do that part) Q_ice + Q_melt + Q_liquid so, it 0.018(2100)T+0.16(4190)T+0.018(334*10^3) but on chegg they didn't use 2100 but they just use 4190 instead and I am confused...
  8. sarahjohn

    Finding Specific Heat of a solid

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

    I RN specific heat

    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...
  10. E

    A query about heat capacity and specific heat capacity

    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 -
  11. E

    Specific heat capacity & heat capacity

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

    Calculating specific heat capacity from entropy

    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...
  13. cwill53

    Specific Heat Capacity Derivation

    The specific heat capacity at constant volume and the specific heat capacity at constant pressure are intensive properties defined for pure, simple compressible substances as partial derivatives of the functions u(T, v) and h(T, p), respectively, $$c_v=\left ( \frac{\partial u}{\partial T}...
  14. jaumzaum

    What chemical properties affect the specific heat?

    Hello all! I would like to know what chemical/physical properties influencies the specific heat. For example, why are specific heat of metals smaller than the specific heat of water, and why do ice and steam have a smaller specific heat than liquid water do.
  15. Y

    Why use c_p and not c_v as specific heat - Thermodynamics

    Hey all, I am working on a problem that goes like this: The cargo space of a refrigerated truck whose inner dimensions are 12 m 3 2.3 m 3 3.5 m is to be precooled from 25°C to an average temperature of 5°C. The construc- tion of the truck is such that a transmission heat gain occurs at a rate...
  16. tanaygupta2000

    Molar Specific heat of Blackbody radiation

    For a body at temperature T, the radiative energy per unit area E depends on 4th power of T. I can obtain expression for specific heat c by differentiating Stefan's law with respect to T. Would it be the correct way of approaching this problem? Or do I need to employ certain models from Solid...
  17. A

    Conceptual thermodynamics question regarding specific heat ratio

    The solution can be found at https://study.com/academy/answer/an-insulated-rigi... After using the two equations I can't see why (h2-h1)/(u2) should equal (T2)/(T1). Can someone explain why specific heat ratio is equal to temperature ratio?
  18. Cammers5

    Specific heat capacity aluminium

    say I used a good insulator?
  19. A

    Specific heat of a monotomic gas

    Given this problem I have calculated the partition function as $$z=1+e^{-\beta E_1}$$ And calculated the average internal energy as $$<U>=\frac{E_1 e^{-\beta E_1}}{1+e^{-\beta E_1}}$$ And thereafter taking the partial derivative of <E> with respect to temp. T the specific heat obtained is...
  20. P

    Constant Pressure Specific Heat in terms of Entropy and Enthelpy

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  21. patric44

    A question about the specific heat and Debye temperature

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  22. Rifat amin

    Below 20K, The specific heat capacity c of silver varies with temperature

    Not attempt
  23. dRic2

    I Lattice specific heat, help understanding a passage in Ziman's book

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  24. TonyKonya

    Specific Heat at High Temperatures

    I am working on some simulations to determine pressures for extremely high-pressure combustion events. The temperatures in these events can range anywhere from 3000 K to 6000 K. In order to do this I need to find valuers for specific heats of gases at these temp ranges as I know they vary to a...
  25. Baibhab Bose

    Phase transition between two phases with different Cv

    I actually can't figure out what kind of phase transition it is and how to proceed through..!
  26. Nikhil Rajagopalan

    Molar specific heat capacity for constant volume.

    Dear Experts, We compute Cv for gases using the idea of equipartition principle and degrees of freedom. In case of a diatomic molecule, there are minimum 3 degrees of freedom (at very low temperatures) and maximum 6 degrees of freedom one of them being vibrational (at high temperatures. Does it...
  27. W

    Calorimetry Lab Analysis (predict specific heat of unknown metal)

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  28. F

    Specific Heat Question

    Homework Statement 1.2.6. Supose that the specific heat is a function of position and temperature, c(x,u). (a)Show that the heat energy per unit mass necesary to raise the temperature of a thin slice of thickness deltax from 0°to u(x,t) is not c(x)u(x,t), but instead int((0->u)c(x,u’))du’...
  29. S

    Can I get specific heat without a final temp? (heat of Rxn)

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  30. A

    Specific heat at constt. volume of an ideal gas

    The ans comes out (c) if I take specific heat at constt volume to be independent of temp. Whether the specific heat is always temp. independent for an ideal gas??
  31. Death eater

    Why the specific heat of solids and liquid does not change?

    Why specific heat of solids and liquids doesn't change with change in temperature?
  32. F

    Problem involving specific heat and graph

    Homework Statement A researcher studies the heat transference between an iron block and an unknown substance, inside an adiabatic calorimeter. In successive experiences he puts inside the calorimeter the unknown substance, always in its solid state and with temperature θs = 20ºC, and the iron...
  33. F

    Specific Heat of a Blackbody

    Hello, I was thinking about how a blackbody (and any other type of body) eventually reaches a steady-state, constant and finite temperature once the absorbed energy is equal to the emitted energy. The specific heat of a substance indicates the temperature change causes by the...
  34. A

    Specific heat capacity of a solid material

    Homework Statement A 4.80 kg piece of solid material is heated from 16.4C to 219C (3 s.f.) using 787 kJ of energy (3 s.f.). Assuming an efficiency of 0.383 for the heating process, and that the material does not melt, calculate the specific heat capacity of the material. Homework Equations...
  35. S

    Calculating Specific Heat Capacity

    Homework Statement A 4.96 kg piece of solid material is heated from 16.7oC to 234oC (3 s.f.) using 725 kJ of energy (3 s.f.). Assuming an efficiency of 0.342 for the heating process, and that the material does not melt, calculate the specific heat capacity of the material. m = 4.96 kg change...
  36. lc99

    Specific Heat problem

    Homework Statement A 12.0 g sample of a metal is heated to 90.0 °C. It is then dropped into 25.0 g of water. The temperature of the water rises from 22.5 to 25.0 °C. The specific heat of water is 4.18 Jg-1°C-1. Calculate the specific heat of the metal. Express your answer in Jg-1°C-1 Homework...
  37. R

    Specific heat

    1. The problem What is the resultant temperature when 100g of steam at 100°C is passed through 500g of ice at -20°C. Homework Equations Q=mCDeltaT[/B] The Attempt at a Solution I am not sure whether both the quantities will combine to from water
  38. G

    Specific heat for an ideal gas

    Homework Statement If Cp for an ideal gas is 35.4 J/mol⋅K, which of the following is Cv for this gas? a. 12.5 J/mol⋅K b. 20.8 J/mol⋅K c. 29.1 J/mol⋅K d. 27.1 J/mol⋅K e. 43.4 J/mol⋅K Homework Equations ΔH = ΔE + Δ(PV) = Q + W + Δ(PV), and for ideal gas, ΔH = nCvΔT + Δ(nRT) = nCvΔT + nRΔT =...
  39. B

    Radiant heat transfer and specific heat

    Homework Statement I'm a little bit stuck with this exercise. A small body with temperature T and emissivity ε is placed in a large evacuated cavity with interior walls kept at temperature Tw. When Tw-T is small, show that the rate of heat transfer by radiation is $$...
  40. P

    Why don't units have match for specific heat and mass

    Homework Statement A problem will ask for an amount of substance in kilograms to be raised to a certain temperature and the specific heat be given in J/g*K. The amount of substance is not required to be converted to grams to match the units in the specific heat to get the correct amount of...
  41. T

    Interpreting Molar Specific Heat number

    Homework Statement Homework Equations Cv=(f/2)R The Attempt at a Solution I have no problem getting the right answers. My question is this: If Cv=72.254 and if Cv = (f/2)R, that implies that f = 17.381. I understand that f represents the gas particle's degrees of freedom. How does this...
  42. HRubss

    Specific Heat Problem, not getting the correct answer

    Homework Statement A copper pot with a mass of 0.500 kg contains 0.170 kg of water, and both are at a temperature of 20.0°C. A 0.250-kg block of iron at 85.0°C is dropped into the pot. Find the final temperature of the system, assuming no heat loss to the surroundings. Homework Equations Q =...
  43. S

    Thermodynamics - Temperature change of Argon

    Homework Statement The temperature of n = 19 mol of argon gas is increased from T1 = 21 oC by Q = 4.4 kJ heat transfer, while the gas pressure is kept constant. What is the new gas temperature in Celsius degrees? Homework Equations and as its a monoatomic gas I think this means that the...
  44. L

    Specific Heat Problem (did something wrong?)

    Homework Statement Heated iron with mass of 55.0 g was added to 100 mL of water at 20 degree Celsius. Assuming no energy transfer to the surroundings and that the final temperature of the system is 42.7 degrees C, calculate initial temperature of the iron. Mass of Iron = 55.0 g mass of Water =...
  45. 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...
  46. yecko

    Specific heat at constant pressure formula help

    Homework Statement https://i.imgur.com/f2vSXtq.png Homework Equations https://i.imgur.com/Kjy1Tzh.png The Attempt at a Solution In this question, the pressure is different at different point, in other words it is not constant throughout the system. Why the solution use c(p) (or "enthalpy" h...
  47. D

    Specific heat of diatomic gases and equipartion energy

    My doubt it is simply if have other reason to don't use this principle for the specific heat of diatomic gases. Homework Equations $$U=NkT=nRT$$ $$u_n=\frac{U}{n}=RT\text{ molar energy}$$ $$u_N=\frac{U}{N}=kT\text{ average energy}$$ $$Z=\sum{e^{-\omega_i/kT}}\text{ with $\omega_i$ particular...
  48. 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...
  49. Const@ntine

    Molecular Specific Heat of an Ideal Gas: Computations

    Homework Statement A cylinder with a heavy ram/piston contains air at T = 300 K. Pi = 2.00 * 105 Pa, Vi = 0.350 m3, Mr = 28.9 g/mol & Cv = 5R/2 (a) What's the Molecular Specific Heat of an Ideal Gas, with a constant volume, computed at J/KgC ? (Cv) (b) What's the mass of the air inside the...
  50. D

    Specific heat in the curve of equilibrium

    Homework Statement Consider a system formed by two phases of a substance that consists of a single class of molecules. Determine the specific heat ##c## of a vapor pressure and temperature ##p## ##T## on the curve of liquid-vapor equilibrium. Consider the steam as an ideal gas. Data: ##c_p##...