Thermo: Deriving dh=Cp(dT) & du=Cv(dT)

In summary: Cp) to the specific heat at constant volume (Cv). This ratio is important in thermodynamics because it relates the amount of energy required to raise the temperature of a substance at constant pressure to the amount required at constant volume.To derive this ratio, we can use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the universal gas constant, and T is temperature.If we divide this equation by the number of moles, we get PV/n = RT, which can be rewritten as P = RT/v, where v is the specific volume (volume per
  • #1
Anony-mouse
60
0
Why does du/dT = Cv, and same for Cp?


Also, i don't understand how Cp/Cv = v, where v is the specific volume. It is derived from:
Cv + R = Cp, how is PV=nRT used to get from Cv + R = Cp to Cp/Cv = v? I know n is replaced by m/M to leave Pv=RT where R would equal R(universal gas const)/M, but how would you use that?


If anyone could please explain any of these things to me i would really appreciate it. This is for a 1st year mech eng undergraduate who has his thermo exam in just over 2 weeks!. cheers.
 
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  • #2
You have to put energy into a system to raise its temperature. Cv is the amount of energy you have to put it to raise its temperature by one degree at constant volume.

Cp is higher, because the system is allowed to expand, which does work on the surroundings. So you have to put in more energy to get the one degree increase in temperature.

It's good that you don't understand Cp/Cv = v, because it's not true.
 
  • #3
Anony-mouse said:
Also, i don't understand how Cp/Cv = v, where v is the specific volume. It is derived from:
Cv + R = Cp, how is PV=nRT used to get from Cv + R = Cp to Cp/Cv = v? I know n is replaced by m/M to leave Pv=RT where R would equal R(universal gas const)/M, but how would you use that?

Cp/Cv is equal to the specific heat ratio, not specific volume.

CS
 

1. What is the meaning of "dh=Cp(dT)" in thermodynamics?

"dh=Cp(dT)" is a mathematical representation of the change in enthalpy (h) of a substance at constant pressure (Cp) as it experiences a change in temperature (dT). This equation is derived from the first law of thermodynamics, which states that the change in internal energy (dU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system.

2. How is "dh=Cp(dT)" derived?

"dh=Cp(dT)" is derived using the definition of enthalpy (h) as the sum of the internal energy (U) and the product of pressure (P) and volume (V). By substituting this definition and the first law of thermodynamics into the equation dU=Q-W, and assuming constant pressure and volume, the equation can be simplified to dh=Cp(dT).

3. What is the difference between "dh=Cp(dT)" and "du=Cv(dT)"?

The main difference between these two equations is the variables used. In "dh=Cp(dT)", the change in enthalpy (dh) is equal to the specific heat at constant pressure (Cp) multiplied by the change in temperature (dT). In "du=Cv(dT)", the change in internal energy (du) is equal to the specific heat at constant volume (Cv) multiplied by the change in temperature (dT). Additionally, enthalpy is a state function that takes into account both internal energy and work done by the system, while internal energy only takes into account the internal energy of the system.

4. How are "dh=Cp(dT)" and "du=Cv(dT)" used in thermodynamics?

These equations are used to calculate the change in enthalpy and internal energy of a substance as it experiences a change in temperature. They are fundamental equations in thermodynamics and are used in various thermodynamic processes and calculations, such as heat transfer and energy efficiency.

5. Can "dh=Cp(dT)" and "du=Cv(dT)" be used for all substances?

No, these equations are specifically derived for ideal gases and may not accurately represent the behavior of other substances. Real gases and substances may have different values for specific heats at constant pressure and volume, which would require different equations for calculating changes in enthalpy and internal energy.

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