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, 18thcentury medical doctor and professor of Medicine at Glasgow University. He measured the specific heat capacities of many substances, using the term capacity for heat.
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...
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...
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...
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##...
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
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...
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)## coordinates then ##A## is the...
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

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...
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,
$$c_v=\left ( \frac{\partial u}{\partial T}...
Hello all! I would like to know what chemical/physical properties influencies the specific heat. For example, why are specific heat of metals smaller than the specific heat of water, and why do ice and steam have a smaller specific heat than liquid water do.
Hey all,
I am working on a problem that goes like this:
The cargo space of a refrigerated truck whose inner
dimensions are 12 m 3 2.3 m 3 3.5 m is to be precooled
from 25°C to an average temperature of 5°C. The construc
tion of the truck is such that a transmission heat gain occurs
at a rate...
For a body at temperature T, the radiative energy per unit area E depends on 4th power of T. I can obtain expression for specific heat c by differentiating Stefan's law with respect to T. Would it be the correct way of approaching this problem?
Or do I need to employ certain models from Solid...
The solution can be found at https://study.com/academy/answer/aninsulatedrigi...
After using the two equations I can't see
why (h2h1)/(u2) should equal (T2)/(T1).
Can someone explain why specific heat ratio is equal to temperature ratio?
Given this problem I have calculated the partition function as $$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...
If ##N## is constant (per the partial derivatives definitions/ the subscripts after the derivatives) then ##G## is constant
##H  TS = constant##
Taking the derivative of both sides with respect to ##T## while holding ##N,P## constant we get the following with the use of the product rule...
this is my attempt of a solution , but my only equation is should i convert Θ to Celsius , and if i did the specific heat of the other
substance is greater , how is that if its inversely proportional with temperature ! . and the other Θ is 200 K so it should be less ?!
Hi, I don't understand why the author in calculating the expression for the specific heat, divides by ##1/V## (the total volume).
Also, in calculating the fraction of modes with frequency in the range ##v##, ##v+dv## he divides by ##V## (eq. 2.65, 2.67)
Thanks,
Ric
I am working on some simulations to determine pressures for extremely highpressure 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...
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...
Problem Statement: so we did an experiment. basically the teacher gave us each a cube of unknown metal
and we had to figure out what it was using the specific heat.
we put the metal in boiling water until it was 212C
and then we put it in room temp water
and we measured how much it heated the...
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’...
Homework Statement
I have delta H _solution, and also the mass of the solitd and q_water and q_reaction.
Im using Dulong Petit to get MM but I need specific heat of the solid obviously.
I don't have a final temp of the unknown solid, just the delta T for the water
thanks for any help
Homework...
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??
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...
Hello,
I was thinking about how a blackbody (and any other type of body) eventually reaches a steadystate, 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...
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...
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...
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 Jg1°C1.
Calculate the specific heat of the metal. Express your answer in Jg1°C1
Homework...
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
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 =...
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 TwT is small, show that the rate of heat transfer by radiation is
$$...
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...
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...
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 0.250kg
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 =...
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...
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 =...
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...
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...
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...
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...
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...
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 liquidvapor equilibrium. Consider the steam as an ideal gas.
Data: ##c_p##...