What is R in the Debye Heat Capacity Equation?

[axawire]

I am currently re-reading an old textbook on thermal physics and they have listed the final result for calculating the Debye Heat Capacity as

C =9R(T/ThetaD)^3*Integral((z^4*e^z dz)/(e^z-1)^2, 0-->ThetaD/T)

But they fail to mention what the R in this equation is, Could some one please tell me what R is?

Thanks.

 

[lightarrow]

I am currently re-reading an old textbook on thermal physics and they have listed the final result for calculating the Debye Heat Capacity as

C =9R(T/ThetaD)^3*Integral((z^4*e^z dz)/(e^z-1)^2, 0-->ThetaD/T)

But they fail to mention what the R in this equation is, Could some one please tell me what R is?

Thanks.

Gas constant. The one in PV = nRT
R = 8.314 Joule/mol°K

 

[astrokreng]

R in the Debye Heat Capacity equation represents the gas constant, which is a fundamental constant in thermodynamics and is denoted by the symbol R. It is a universal constant that relates the energy of a system to its temperature and is equal to 8.314 J/mol.K. It is also known as the molar gas constant as it is the same for all gases and is used to convert between energy and temperature units in thermodynamic calculations. Therefore, in the Debye Heat Capacity equation, R is used to relate the heat capacity of a substance to its temperature and the Debye temperature.