Heat Capacity and First Thermodynamic Law

In summary, The way to deduct the First Thermodynamic Law is given by: @constant volume,Qv=Cv(T2-T1)Because W=0, E2-E1=Cv(T2-T1)After all, Cv=d(E2-E1)/d(T2-T1)@constant pressure,Given that E2-E1=Qp-P(V2-V1) and Qp=Cp(T2-T1)We have Cp(T2-T1)=(E2-E1)+P(V2-V1
  • #1
FriedrichLuo
3
0
I have a question about the deduction of First Thermodynamic Law. The book that I have is written by Paul A. Tipler and Gene Mosca and it is called Physics: For Scientists and Engineers.

The way to deduct it is given here:

@constant volume,
Qv=Cv(T2-T1)
Because W=0, E2-E1=Cv(T2-T1)
After all, Cv=d(E2-E1)/d(T2-T1)

@constant pressure,
Given that E2-E1=Qp-P(V2-V1) and Qp=Cp(T2-T1)
We have Cp(T2-T1)=(E2-E1)+P(V2-V1)
Now, the author replaces E2-E1 with Cv(T2-T1), I cannot understand this because he incites something under constant volume into a formula under constant pressure.

My question is what determines the internal heat in a system is defined by CvP, which can even be used in a situation in which a different condition is given.

Please help me if you know! Thank you in advance!
 
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  • #2
Hi FriedrichLuo, welcome to PF. Yours is a very common question, as it is disconcerting to see a "constant-volume" parameter being used in a constant-pressure process. But energy is a state variable (its value is process independent), and for this system the relationship E2-E1 = Cv(T2-T1) holds for all processes.
 
  • #3
Mapes said:
Hi FriedrichLuo, welcome to PF. Yours is a very common question, as it is disconcerting to see a "constant-volume" parameter being used in a constant-pressure process. But energy is a state variable (its value is process independent), and for this system the relationship E2-E1 = Cv(T2-T1) holds for all processes.

Hey, Mapes. Thank you for your reply! I come down to this after reading your post:

dU=dQ+dW, dU is a state parameter and dQ and dW are process parameters. Therefore, dQ(or Cv(T2-T1) holds for any situations where process is involved. And dU is a result when a new state is reached. In other words, dQ and dW are what is really happening; dU is only concept to show the resultant of two true processes.

I hope I get it right. :D
 
  • #4
This sounds like a fine way of thinking about things, but make sure you don't mix your differential and finite values. You can say

[tex]\delta Q=C_V\,dT[/tex]

or

[tex]Q=C_V(T_2-T_1)[/tex]

but not mix them.
 

FAQ: Heat Capacity and First Thermodynamic Law

1. What is heat capacity?

Heat capacity is the amount of energy required to raise the temperature of a substance by one degree. It is a measure of how much heat a material can hold.

2. How is heat capacity related to the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted. Heat capacity is related to this law because it measures the amount of energy needed to raise the temperature of a substance, which is a form of energy transfer.

3. What factors affect heat capacity?

The main factors that affect heat capacity are the mass and composition of the substance, its temperature, and any phase changes that may occur. Additionally, the type of material and its physical properties, such as density and specific heat, can also impact heat capacity.

4. How is heat capacity measured?

Heat capacity is typically measured using a calorimeter, which is a device that can accurately measure the heat gained or lost by a substance. The substance is heated or cooled, and the change in temperature is recorded. From this, the heat capacity can be calculated using the equation Q = mcΔT, where Q is the heat, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.

5. How does heat capacity differ from specific heat?

Heat capacity and specific heat are related but not the same. Heat capacity is the amount of energy needed to raise the temperature of a substance by one degree, while specific heat is the amount of energy needed to raise the temperature of one gram of a substance by one degree. Heat capacity is an extensive property, meaning it depends on the amount of substance, while specific heat is an intensive property, meaning it is independent of the amount of substance.

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