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. M

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. 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. 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. 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. 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. Why Is My Calculation of Heat Energy Incorrect?

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. 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. 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 Calculating the Area of an RN Event Horizon with Specific Heat Formula

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. 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. 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. 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...

40. 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. 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. 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. 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. 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##...