Specific heat Definition and 481 Threads

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




c

p




{\displaystyle c_{p}}
and




c

V




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



γ
=

c

p



/


c

V




{\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. P

    Specific Heat and Helmholtz Free Energy?

    I'm wondering if there's a simple relation between the specific heat capacity (at constant chemical potential) and the Helmholtz Free Energy? I can't seem to find a relation in the literature between these three quantities, specifically.
  2. K

    Maximum mass of a metal you can melt; Heat of Transformation

    Homework Statement What is the maximum mass of lead you could melt with 2000 J of heat, starting from 25 ∘C ? Lead melts at 328∘C , its specific heat is 128 J/(kg⋅K) , and its heat of fusion is 2.5×10^4 J/kg . Homework Equations Need to find both the mass in the heat of transformation (Q =...
  3. I

    Why Does Iron Have a Higher Molar Specific Heat Than Its Debye Value?

    Why does iron have molar specific heat greater than Debye value 3R?
  4. M

    Find the molar specific heat for each gas.

    Homework Statement A mixture of two ideal gases, the first one atomic and the second two atomic are put in normal conditions in a calorimeter with volume 1 liter hermetically closed. After it is given 10J thermal energy the mixture temperature is grown 14.2 K. Find the molar specific heat for...
  5. T

    Determination of specific heat in a reaction

    Is there a way to determine the specific heat of a reaction before said reaction is introduced. thanks in advance for all of your inputs.
  6. J

    T/F The specific heat of copper is about 3R

    Homework Statement This was a problem I had on a stat mech exam awhile ago and I never figured out how to answer it. It asked "True or false, the specific heat of copper at room temperature is approximately ##3R##". Homework Equations $$C=\frac{Q}{\Delta T}$$ The Attempt at a Solution...
  7. 1

    Debye's T^3 Law: Specific heat, Latice and Electronic terms

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  8. L

    Specific heat capacity of gases

    Homework Statement Figure shows two rigid vessels A and B, each of volume 200 cm3 containing an ideal gas (Cv = 12.5 J/mol-K). The vessels are connected to a manometer tube containing mercury. The pressure in both the vessels is 75 cm of mercury and the temperature is 300 . (b) 5.0 J of heat...
  9. Eclair_de_XII

    How do I find the specific heat of a hot object in water?

    Homework Statement "Using the above calorimetre with 100.0 g of water of in it at 20.0°C, a 50.00 g sample of a metal at 100.0°C is added. The temperature of the calorimetre rises to 27.2°C. What is the specific heat? (S.H. = 0.20 cal/g°C)" Homework Equations Heat capacity of calorimetre used...
  10. D

    Specific heat capacity and changing volume

    Hello everyone, I just need some help understanding some thermodynamics. So I have 0.25 kg of helium which is compressed from an initial state in a polytropic process with n = 1.3. So its given the change in volume and the initial pressure. I need to find the change in internal energy. I am...
  11. A

    Hydrogen and it's Specific Heat.

    Hello, I had a few questions regarding hydrogen. I know for a fact that hydrogen has a high value of specific heat. My questions are: 1). Isn't hydrogen supposed to be a good coolant, and if it is is it actually used ? 2). If it is a good coolant how does it work as a fuel ? I hope these...
  12. S

    Specific Heat at constant pressure for photon gas

    Homework Statement A blackbody photon gas is contained within an evacuated cavity (V = 0.01 m^3). Calculate C_p for the photon gas at T = 1000K Homework Equations C_p - C_v = T(\frac{\partial S} {\partial V}) (\frac{\partial V}{\partial T}) C_v = T(\frac{\partial S} {\partial T}) S =...
  13. R

    Specific heat capacity ; voltage ; heating water

    Hi, I am doing an experiment on the factors affecting the time to heat water from a set temperature to another, eg 20 to 35 deg C. 1. First, I have insulated the beaker properly, to minimise heat loss. I have connected a heating element to heat the water. Connected multimeter, give the voltage...
  14. G

    How Do I Determine the Change in Entropy of the System?

    Homework Statement Determine ΔSsys when 3.0 mol of an ideal gas at 25°C and 1 atm is heatedd to 125°C and expanded to 5 atm. Rationalize the sign of ΔSsys. Homework Equations State Function: dS = (dU)/T + (PdV)/T State Function for Entropy of Ideal Gas: dS = (CV,mdT)/T + (nRdV)/V Ideal gas...
  15. Muhammad Nauman

    Specific heat capacity of Gd5Si3 and GdSi

    Hello alll. I am Muhammad Nauman, Research Associate in COMSATS university islamabad pakistan and new in this group. I need Specific heat capacities of Gd5Si3 and GdSi. Can someone help me??
  16. D

    Specific Heat Capacity of water in a kettle

    Homework Statement mass, m, of water in kettle 1.5 kg power rating, P, of kettle 2.1 kW time interval, t, for heating 322 seconds starting temperature 4 °C = 277 K finishing temperature 100 °C = 373 K temperature change, ΔT 96 K electrical energy supplied, E = P × t...
  17. Suraj M

    Why is the molar specific heat of carbon so different from the predicted value?

    why is the molar specific heat of carbon(=6.1JMol-1K-1) so different from the predicted value of 3R≈25??
  18. kelvin490

    Internal Energy & Ideal Gas: Is dH=Cp dT Always?

    For an ideal gas, the internal energy is a function only of temperature, so that dU = CvdT can always be applied. I am not sure whether dH=CP dT is also always true even the pressure is not constant.
  19. S

    Calculating Mass Increase of Coffee Using Specific Heat Capacity

    Homework Statement Using coffee (specific heat capacity of 3.98 x 10^3 J/kg °C) calculate the increase in mass if you raised the temperature of a 353 g cup of coffee from 34° C to 97°C. Homework Equations Q=mcΔt The Attempt at a Solution I believe I just need to solve for m. However I have...
  20. C

    Phonon contribution to specific heat of solids

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  21. R

    Specific heat Capacities of metals

    Hi Admin, please allow me to post this here: The General Formula for Specific Heat Capacity is: C(Total) = C(electron)+C(phonon) C(electron) = aT where a is the sommerfield constant. C(phonon) = bT^3 this time i don't know what is b (some constant) so my problem is, how can i determine b...
  22. R

    Thermodynamics : molar specific heats for gases

    Homework Statement An audience of 2750 fills a concert hall of volume 35000 m3. If there were no ventilation, by how much would the temperature of the air rise over a period of 2.0 h due to the metabolism of the people (70 W/person)? Homework Equations Q= nCvΔT Cv= (3/2) R The Attempt at a...
  23. H

    Ring and Sphere Linear Expansion

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  24. K

    Finding the Specific Heat Capacity of a Potato

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  25. R

    Calculating Specific Heat Capacity: Solving for Unknown Variables

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  26. T

    Calculating Heat Transfer in Melting Ice: A Thermochemistry Problem

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  27. U

    How Do You Calculate the Final Mass of Water in a Calorimetry Experiment?

    Homework Statement A 0.080kg copper container (specific heat: 387Jkg-1K-1) contains 0.30kg of water and 0.040kg of ice at 0°C. Steam at 100°C is passed into the water and its temperature stabilizes at 20.0°C. Find the mass of the water left in the container assuming the system is insulated...
  28. mef51

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  29. A

    Specific Heat Capacity of water

    The specific heat capacity of water is accepted to be roughly 4.18 J/gK. How would the specific heat value of a given water sample be effected when sediments and other forms of particulation, such as iron oxide from rust, are present? Would the mixture have a higher specific heat capacity value...
  30. P

    The temp. dependent Specific heat and expansion coefficient of Cobalt?

    Hey. I am writing my master thesis, and I really need to find the temperature dependent heat capacity and expansion coffient for Cobalt. I have tried searching the internet, whitout luck. Please, can anybody help me. It is really important!
  31. S

    Specific heat capacity of copper

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  32. F

    Specific Heat Capacity: Comparing Spheres

    How do I know which one of these two spheres have more specific heat capacity?
  33. I

    Specific Heat of a nonlinear, temperature dependent spring

    Homework Statement A nonlinear spring has a temperature dependent force law, F = -\frac{K}{T}(L-L_o)^3 At a temperature T = T_o and length L = L_o the specific heat at a constant length is C_L = C_o. What is the specific heat at T = T_o when the spring is stretched to length 2L_o...
  34. A

    Specific heat capacity of liquid form of permanent gases.

    Hi, The permanent gases like Nitrogen, Helium etc. have more specific heat capacity as liquid than their gases. Seemingly degree of freedom should reduce in liquid form, and therefore, specific heat capacity must reduce in liquid form. But this isn't the case. I remember reading somewhere...
  35. S

    Specific heat capacity - heating ice/water

    Homework Statement A pot on a stove burner contains 10kg of water and an unknown mass of ice at equilibrium at 0degC at time = 0min. During the first 50mins, the mixture remains at 0degC. From 50 to 60mins the temperature increases to 2degC. What is the initial mass of ice? Ignore the heat...
  36. S

    Specific heat capacity - heat energy transfer

    Homework Statement Find the mass of water that vaporizes when 3.39 kg of mercury at 243 °C is added to 0.476 kg of water at 90.0 ° Homework Equations q=mcT, q=mL The Attempt at a Solution When vaporising T=100degC. Heat lost by mercury = heat gained by water. 3.39kg x 139J/kg/C x...
  37. le@rner

    Specific Heat Capacities in co-ordination with Thermodynamics

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  38. S

    Specific Heat Capacity: Why Do Some Substances Take More Energy?

    When two substances have the same temperature, the particles have the same average kinetic energy, right? So why is it that some substances take more energy to increase the temperature one degree even if the increase in average kinetic energy is the same? I'm referring to specific heat...
  39. H

    Comparing Specific Heat Capacity of Metals A & B in Wax Block

    Homework Statement the answer is c) but i can't figure why ! is the more heat capacity substance lose and gain energy faster than the other one so it take more energy to get it's temperature raised by the same amount because it lose most of it very fast during the heating process ?
  40. N

    How to determine specific heat capacity

    I have been looking for specific heat capacities of certain materials such as steel but i can never find a solid answer, so i figured i would test it myself, how would one test specific heat capacities?
  41. T

    Specific Heat in Absolute vs Relative Units

    I'm running a simulation on a gas mixture that spits out its Specific Heat in a number of different units. The values for Specific Heat in Btu/lbmolF vs Btu/lbmolR are the same, which confuses me at first glance. I sort of remember in Thermo not having to worry about Btu/lbmolF vs...
  42. P

    The specific heat capacity at constant volume for liquid isopropanol?

    Hey I am a physics student, and not so familiar with chemistry. I have a huge problem, because I have to find the following 3 values for liquid isopropanol: 1. The specific heat capacity at constant volume 2. The specific heat capacity at constant pressure 3. Volumetric Isobaric...
  43. C

    Problem on entropy change and specific heat capacity

    Calculate the change in entropy of the Universe as a result of the following operations: (a) A copper block of mass 0.4kg and thermal capacity 150JK-1 at 100◦C is placed in a lake at 10◦C. dS=dQ/T dQ=mCdT Tried simply combining these equations and integrating to find change of entropy of...
  44. U

    What is the specific heat of the liquid?

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  45. koustav

    Van der waals equation and molar specific heat

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  46. T

    Master Specific Heat Calculations: Answers in SI Units

    have two specific heat questions that I am having trouble with. Though i thought this was a chemistry topic, we are learning it in my physics class as well 1. The specific heat of aluminum is 0.22 cal/g *C What is the specific heat in Btu/lb*F The Fahrenheit is the part that I...
  47. G

    Heat Capacity and specific heat

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  48. D

    What is the Final Temperature When Ice, Water, and an Iron Container Interact?

    Homework Statement A 30.0g block of ice at 0.00°C is dropped into 500.0g of water at 45.0°C. If the process was carried out in an iron container with a mass of 150g what would the final temperature be? Homework Equations Q=mc(T2-T1) Heat Lost = Heat Gained Specific Heat of Water: 4200 Specific...
  49. Kelsi_Jade

    Van der Waals Equation and specific heat

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