Thermodynamics: Entropy and specific heat

[Pandris]

Hi here!

(before scriptum. Sorry for my lousy English and LaTex.)

I am a bit confused about entropy change statements:

In most textbooks is given:
$$\Delta S = n (C_V ln \frac{ \ T_{2}}{T_1} + R ln \frac{ \ V_{2}}{V_1})$$

where n - moles of gas. And dimension of entropy is [J/K]

But now I have one book there entropy change is defined using specific heats:

$$\Delta S = m (c_v ln \frac{ \ p_{2}}{p_{1}} + c_p ln \frac{ \ V_{2}}{V_{1}})$$

where m - mass of gass, and dimension is [J/(kmol*K)]

I can't understand where this isobaric specific heat gets here!

Ok, I understand that these entropies essentially are given for different measures of amount of gass. First is given for moles, but second for kilograms. (am I right??)

But how to involve specific heats there is obscure for me.

Thanks!

 

[Pandris]

Oh my!

Am I blind or what?!

Everything works out if take in mind that
$$C_p - C_V = R$$
and

$$c_v = \frac { \ C_{V}}{ \mu}$$

That's it! Sorry for buzzer!

 

[kyle8921]

Hi there,

First of all, your English and LaTex are perfectly fine, so no need to apologize!

To understand the difference in the two equations for entropy change, we need to first understand the concept of specific heat. Specific heat is the amount of heat required to raise the temperature of a unit mass of a substance by one degree. It is a property of the substance and is usually denoted by the symbols c or C.

In the first equation, the change in entropy is given in terms of moles of gas, which is a measure of the amount of gas. This equation takes into account the change in temperature and volume of the gas, as well as the gas constant (R). The gas constant is a universal constant that relates the energy of a system to its temperature and is used to convert from moles to mass in the second equation.

In the second equation, the change in entropy is given in terms of mass of gas, which is a measure of the amount of substance. This equation takes into account the change in temperature and volume of the gas, as well as the specific heats (c_v and c_p). The specific heats are used to convert from mass to moles and take into account the amount of heat required to raise the temperature of a specific mass of a substance.

To summarize, the first equation is used when the amount of gas is measured in moles, while the second equation is used when the amount of substance is measured in mass. The specific heats are used to convert between these two measures of amount. I hope this helps to clarify the use of specific heats in the equations for entropy change. Let me know if you have any further questions.

Best regards,