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EastWindBreaks
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Homework Statement
Homework Equations
The Attempt at a Solution
U is internal energy, but what is u? if its internal energy at a specific state, then why its multiplied by mass? does not makes sense to me...
sorry, the question is : A piston-cylinder device contains 0.95 kg of oxygen initially at a temperature of 27 Celsius and a pressure, due to the ambient atmospheric pressure and a weight on the top of the piston, of 150 kPa. Heat is added to the gas until it reaches a temperature of 627 Celsius . Determine the amount of heat added to the gas during the process.mfb said:Looks like the specific energy. More context would help.
u is the internal energy per unit mass.EastWindBreaks said:Homework Statement
Homework Equations
The Attempt at a Solution
U is internal energy, but what is u? if its internal energy at a specific state, then why its multiplied by mass? does not makes sense to me...
For an ideal gas, the internal energy is a function only of temperature (and not volume). So it doesn't matter whether the volume changed. The subscript v on Cv refers to how this quantity is measured experimentally in the laboratory (by determining the amount of heat Q needed to raise the temperature of a material at constant volume, i.e., in a test where ##Q =\Delta U=mc\Delta T##), and not how Cv is applied in practice for more general situations (where ##Q\neq\Delta U##).EastWindBreaks said:sorry, the question is : A piston-cylinder device contains 0.95 kg of oxygen initially at a temperature of 27 Celsius and a pressure, due to the ambient atmospheric pressure and a weight on the top of the piston, of 150 kPa. Heat is added to the gas until it reaches a temperature of 627 Celsius . Determine the amount of heat added to the gas during the process.
Q-W=Delta U
how does delta E= delta U= m(u2-u1)=m*c*(T2-T1)?delta U = Q is only correct under constant volume, for which has no work. so, since this thing is changing its volume, what happened to the work done by the system, its not in the equation. (this is from the book),as far as I know, m*c*(T2-T1) is just Q, heat energy.
and yeah, u as specific energy makes sense to me...just first time seeing specific energy. Thank You!
whitsona said:Found an answer for you. Sorry to refer you to Wikipedia. But, their page on isobaric processes derives this for you. Note that you are using the OTHER specific heat. :-) There is cv and there is cp. I'm sorry to be so rusty! Too many years in engineering management. Sad, really.
Chestermiller said:For an ideal gas, the internal energy is a function only of temperature (and not volume). So it doesn't matter whether the volume changed. The subscript v on Cv refers to how this quantity is measured experimentally in the laboratory (by determining the amount of heat Q needed to raise the temperature of a material at constant volume, i.e., in a test where ##Q =\Delta U=mc\Delta T##), and not how Cv is applied in practice for more general situations (where ##Q\neq\Delta U##).
No. Delta U is equal to Q only if no work is done. But, for an ideal gas, ##\Delta U=nC_v\Delta T## always. So, for an ideal gas, ##Q=nC_v\Delta T## only if no work is done. You must learn to associate Cv with U, and must stop associating Cv with Q. Otherwise, this is going to drive you crazy.EastWindBreaks said:sorry, I am still a little confused, are you saying that for an ideal gas, Delta U simply equals Q?
The work contributes to internal energy through the first law equation ##\Delta U=mC_v\Delta T=Q-W##. Note that in this equation, if work is done, the internal energy is affected.but if the volume changes as it is for this problem, the work done does not contribute to the internal energy of the system?
Yes, in the sense I just mentioned.i thought work can raise temperature as well?
This equation is always correct for the case of an ideal gas. It can be regarded as the definition of Cv. Back to the first law. If W = 0, then ##\Delta U=Q##. This is the only circumstance in which we also find that also ##Q=nC_v\Delta T##.On Wikipedia it states " assuming that the quantity of gas stays constant, e.g., there is no phase transition during a chemical reaction. According to the equipartition theorem, the change in internal energy is related to the temperature of the system by
,
where cV is specific heat at a constant volume."
I have never heard of equipartition theorem, I looked into its page, but didn't find an explanation for how delta U is just Q where work is not considered.
Chestermiller said:In summary, for an ideal gas,
1. ##\Delta U## is always equal to ##nC_v\Delta T##
2. Q is equal to ##nC_v\Delta T## only if no work is done
For an ideal gas, internal energy is a function only of temperature. So, no, constant volume is not required in order for ##\Delta U=nC_v\Delta T##. Like I said(several times), this equation applies irrespective of whether volume is constant. I don’t know how many different ways I can say this.EastWindBreaks said:I see, constant volume = no work, that makes sense that ΔU=mCvΔT. But for this problem, one of the step in the book wrote ΔU=mCvΔT, the volume does change though...the pressure is constant.
but it was ##\Delta U=mC_v\Delta T## in the book, m not nChestermiller said:For an ideal gas, internal energy is a function only of temperature. So, no, constant volume is not required in order for ##\Delta U=nC_v\Delta T##. Like I said(several times), this equation applies irrespective of whether volume is constant. I don’t know how many different ways I can say this.
Whichever you prefer.EastWindBreaks said:but it was ##\Delta U=mC_v\Delta T## in the book, m not n
m and n are completely different though, m for mass, n for number of moles,Chestermiller said:Whichever you prefer.
So, if you use m, then you use the heat capacity per unit mass, and if you use n, then you use the heat capacity per mole.EastWindBreaks said:m and n are completely different though, m for mass, n for number of moles,
I finally got it, with molar heat capacity being capital letter C and specific heat per unit mass being lower case c, I didn't know there are 2 version of heat capacities, thank you!Chestermiller said:So, if you use m, then you use the heat capacity per unit mass, and if you use n, then you use the heat capacity per mole.
In this equation, "u" represents the internal energy of the system.
The "u" is squared because it represents the square of the speed of the particles in the system and is a measure of the kinetic energy of the system.
"u" is directly related to the temperature of the system. As the temperature increases, the average speed of the particles (represented by "u") also increases, resulting in a higher internal energy.
"u1" and "u2" represent the initial and final internal energies of the system, respectively. The difference between these two values represents the change in internal energy (delta U) of the system.
Yes, this equation can be applied to all systems, regardless of their size, shape, or composition. It is a fundamental equation in thermodynamics and is used to calculate the change in internal energy of a system.