What is Specific heat capacity: Definition and 198 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

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. 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. 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
5. 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 -
6. 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
7. Calculate the Mass of Ice cubes needed to cool a soft drink

Summary:: TLDR : Drink cooled from 17 C to 7 C with either ice cubes (method 1) or soapstone stones (method 2). Calculate the mass of each item that would be needed to cool the same drink. Given the information provided. In order to cool a drink (“cola” for example) from a storage-room...
8. 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...
9. Engineering Thermodynamics, Calculating the required mass flow

I have solved this question and it seemed pretty easy, but I got an extremely large number for the mass flow, I had to post the question here to make sure I did it correctly. Any help will be appreciated.

11. How do you approximate between the Cp of a gas and a solid?

I have the Cp of Benzoyl peroxide (BPO) in gas form (454.39 J/molK). What approximation could I make to find the Cp of solid BPO as I cannot find this info online? thanks

31. 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...
32. 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...
33. 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...
34. 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...
35. Specific Heat Capacity Graph Question

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36. 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...
37. 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...
38. 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...
39. 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=...
40. 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...
41. Clarification on derivations of specific heats in fluids

Hello! I understand what specific heats are and how to derive them. I just feel that I'm missing a little something in the methodology. Consider the 1st law of thermodynamics and the definition of enthalpy: 1) dU = δQ -δW = δQ - PdV 2) H = Q - VP For the derivation of CV, dV = 0 and the...
42. 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...
43. Specific heat capacity coursework

Homework Statement earlier today i was doing some coursework to find the specific heat capacity of an unknown metal by submersing 100g / 0.1kg of the metal in boiling water above 75°C and record the temperature after 30 seconds (θm). we then had to transfer the the metal from the boiling water...
44. Specific heat capacity (the very basics)

The specific heat capacity is the amount of heat energy needed to raise 1 kg of a substance by 1 °C. Q. So the specific heat capacity of water is 4.184kJ (given that 1 Cal (large calorie aka the kg calorie aka the food calorie) is required to do the same, ie, raise the temperature of 1 kg of...
45. Specific heat capacity of calorimeter

I've got a problem: A piece of copper with mass m1 = 800 g and temperature t1 = 80 ° C is placed in a container with good thermal insulation. The vessel initially contains water with mass m2 = 500 g temperature t2 = 20 C. What is the calorimeter (including thermo meter) heat capacity if the end...
46. Specific heat capacity of metal

Homework Statement I have 1.5 kgs of silicon with temperature 40 degrees celsius. It is dropped into 3 kgs of water holding temperature 25 degrees celsius. The system is heat isolated from the environment and the final temperature of the system is 26.2 degrees celsius. I need to find the...
47. Heat Exchange and Efficiency in a Fridge

Homework Statement In a 30% efficient, -16°C fridge, how much electrical energy will be used up to lower the temperature of 250 mL of 75°C water? If the fridge is rated at 150 W, how long will this process take? Specific Heat Capacity of Water = 4200 J/Kg×K Specific Heat Capacity of Ice = 2000...
48. 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...
49. 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...
50. 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...