Internal Energy Thermodynamics

In summary: Then the integrals reduce to simple products, as you know. In this case, you would use:$$\Delta U=nC_v\Delta T$$$$\Delta H=nC_p\Delta T$$But, depending on the problem, you may need to integrate. In this case, you need to integrate according to the temperature dependence of the heat capacities. So, you need to look up the temperature dependence of the heat capacities and integrate that way. Does that help?In summary, in this problem, CO2 at P=3atm, T=295K, and V=1.2m3 is isobarically heated to T=500K. To find ΔU and
  • #1
dlacombe13
100
3

Homework Statement


CO2 is at P=3atm, T = 295K and V=1.2m3.
It is isobarically heated to T = 500K.
Find ΔU and ΔH

Homework Equations


dU = cpdT

The Attempt at a Solution


I am having a hard time in general in this class. I understand that in this problem, ΔP = 0. Does this mean that there must be a ΔV? Also, I am having a hard time understanding how to use cp if in this case, it changes with temperature. I do not think I need to use integration, but I am not sure.
 
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  • #2
dlacombe13 said:
I understand that in this problem, ΔP = 0. Does this mean that there must be a ΔV?
Yes.

dlacombe13 said:
Also, I am having a hard time understanding how to use cp if in this case, it changes with temperature. I do not think I need to use integration, but I am not sure.
If ##c_p## changes with temperature, then you need to integrate.
 
  • #3
dlacombe13 said:

Homework Statement


CO2 is at P=3atm, T = 295K and V=1.2m3.
It is isobarically heated to T = 500K.
Find ΔU and ΔH

Homework Equations


dU = cpdT
No. dU = nCvdT

The Attempt at a Solution


I am having a hard time in general in this class. I understand that in this problem, ΔP = 0. Does this mean that there must be a ΔV?
CO2 can be treated as an ideal gas, so: PV = nRT. If T increases and P stays the same, what happens to V?
Also, I am having a hard time understanding how to use cp if in this case, it changes with temperature. I do not think I need to use integration, but I am not sure.
Cp is the heat capacity at constant pressure. So multiplying Cp by the change in temperature and number of moles gives you ...?. Since H = U + PV, can you determine the ΔH? (Hint: for constant pressure changes, how is it related to ΔQ?). Use ΔU = nCvΔT to determine change in internal energy.

AM
 
  • #4
dU = cpdT wasn't that dH :smile: ?
dlacombe13 said:
Does this mean that there must be a ΔV?
Yes. Ideal gas law is good enough.
dlacombe13 said:
Also, I am having a hard time understanding how to use cp if in this case, it changes with temperature. I do not think I need to use integration
Either you integrate (stepwise), or you look it up. it indeed changes with T

dlacombe13 said:
I am having a hard time in general in this class
That's OK. With thermodynamics the sequence is: completely disoriented, then gradually more confident, and -- by the time you Master it -- complete disorientation again :smile:

[edit] wow, three responses !
 
  • #5
Okay so I am familiar with the PV=nRT formula. In our class, we usually use PV=mRT, and use the specific R for the gas in question. Would my first step be to calculate the mass of CO2 in state 1 using this formula?
 
  • #6
dlacombe13 said:
Okay so I am familiar with the PV=nRT formula. In our class, we usually use PV=mRT, and use the specific R for the gas in question. Would my first step be to calculate the mass of CO2 in state 1 using this formula?
Yes. Does the mass change?

AM
 
  • #7
No I wouldn't think that mass would change. I went ahead and calculated the volume of the second state, although I'm not sure if it was needed. Would I then have to use dU = mcvdT ? And since it cv is not constant, would I need to integrate both sides of this equation?
 
  • #8
I am confused because I do not understand which value to choose for Cp if it changes with volume. Even if I were to integrate I would have:
∫dU = m∫Cp dT
But how can I do that? The Cp is really throwing me off, and I have no idea how to use it in this problem. The same goes for Cv, since that also changes with temperature. Any help?
 
  • #9
For an ideal gas, Cv and Cp are both functions only of temperature. They are related to the changes in internal energy and enthalpy by:
$$dU=nC_vdT$$
$$dH=nC_pdT$$
If the heat capacities are functions of temperature, then, to be exact, you need to integrate. But, often, if the temperature interval is small, the heat capacities can be approximated as being constant.
 
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1.

What is internal energy in thermodynamics?

Internal energy is a thermodynamic property that represents the total energy of a system, including its microscopic kinetic and potential energies. It is a state function, meaning it depends only on the current state of the system and not on how the system got to that state.

2.

How is internal energy related to temperature?

According to the first law of thermodynamics, the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system. When the system undergoes a change in temperature, the internal energy also changes. As temperature increases, so does the internal energy.

3.

What is the difference between internal energy and enthalpy?

Enthalpy (H) is another thermodynamic property that takes into account not only the internal energy of a system but also the pressure and volume of the system. It is defined as H = U + PV, where P is pressure and V is volume. In other words, enthalpy is the internal energy of a system plus the energy required to push back the atmosphere and make room for the system.

4.

How is internal energy affected by changes in a system?

Internal energy can change in a system due to the addition or removal of heat, or mechanical work. It can also change during phase transitions, such as melting or boiling. The specific heat capacity of a substance also plays a role in how much the internal energy changes with a given amount of heat added or removed.

5.

Can internal energy be measured directly?

No, internal energy cannot be measured directly. It is a state function and therefore only the change in internal energy can be measured. However, the change in internal energy can be calculated by measuring the heat and work exchanged by the system.

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