For the majority of gases, Cp is greater than Cv. For an ideal gas, the relationship is Cp - Cv = R (the gas constant). For liquids, the relationships are somewhat more complex, but in general, here also Cp > Cv.
Stephen.
For the gases, Cp is greater than Cv. For an ideal gas, Cp - Cv = R
I think that we have answered your question, at least for ideal gases unless you want to expand the expressions to something along the lines of:
I have overlooked the answer that you require which is "more than" in most cases.
For Gas:
The pressure and volume change in temperature and the amount of heat required to raise the temperature for 1(gmol) of gas through 1°C depends on the way gas is heated.
Specific heat possesses infinite values. The specific heat of the gas is not constant. If you supply heat at constant pressure, you must have Cp. If you supply heat at constant volume, you must have Cv. For an ideal gas:
Cp – Cv = nR, where n is amount of substance, R:8.314 J /(mol K ).
Therefore, Cp is greater than Cv for gases.
For Solids and liquids:
The volume and the pressure of solid remains constant when heated through a small range of temperature. So, Cp=Cv.
In Thermodynamics, for ideal gases, the relation between Cp and Cv is defined as:
Cp-Cv=R
Where R is a ideal gas constant and is equal to 8.31 J/MK.
Thus, Cp=Cv+R
Or Cp is greater than Cv.
Well, having said it all by researchers above, Cp is morethan Cv for ideal gases scenario, based on the established convention i.e. Cp - Cv = R. Where R is the universal gas constant with a standard value of 8.31J/mol.K. Similarly, Cp/Cv = Gamma, with the Gamma value varying depending on the atomic state and condition of the concerned gas, but always greater than one.
Cp = Cv + P (δV / δT) p, the latter being P (δV / δT) p, the amount of work produced or received by the system
Well in general, Cp= Cv + R as we know. And R can be defined as P(deltav/deltaT)p as some fellow researchers have pointed.
Thus for Cp=Cv, its necessary for R to be zero. Meaning deltav being zero. Meaning the substance be incompressible. Which generally counts towards solids.
The ratio of specific heat at constant pressure to the specific heat at constant volume is always greater than one.
As, when the gas is allowed to expand resulting in constant pressure, some of the heat is converted to work resulting in the need of a higher amount of heat to raise the temperature of the gas. Whereas when the volume of the gas is constant, the entire heat supplied is utilized in raising the gas temperature. Hence the heat required the raise the temperature of a unit mass of gas at constant pressure is greater than that required at constant volume. Hence the ratio c
p
:c
v
is always greater than one.
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