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For class we have been asked to show how the first lawFirst Law of thermodynamics.

dU=dQ+dW$$\mathrm dU = \mathrm dQ + \mathrm dW$$

can be shown to be

dQ=(CV/R)*VdP +(Cp/R)*PdV$$\mathrm dQ = \frac{C_V}{R}V\,\mathrm dP + \frac{C_p}{R}P\,\mathrm dV$$

assuming a closed system.

I have an answer, but am hesitant to say it is a final answer or even the correct one at that.

I will admit that while doing the problem I had trouble following what I was doing. Hence my posting the question. It seemed to me that because we know how state functions act and change with certain processes, that much of the problem is a more of a "plug and chug" approach.

But, I am concerned with the partial derivatives when rearranging this equation. How do certain parts cancel out or how does one approach the problem without them? Is it safe to assume that since you know how the state variables will act in a certain process, that you can use that knowledge to provide a better or more exact answer to the problem?

Attached you will find a picture of the problem that I have done to the best of my ability (which is limited I must say).

If anyone can provide an explanation as to why certain things are done the way they are, or correct my dissection of this problem, I would be grateful for your time in the matter.

What I am looking for in particular, is how do I make my assumptions? Do I assume holding one constant to solve the equation in one way, i.e. adiabatic process, isothermal process, etc. Then do the same for another path and compare?

p.s. The last bit of the problem asked to show how PV^gamma=Constant and can be disregarded.

enter image description hereWorking for above proof

For class we have been asked to show how the first law of thermodynamics.

dU=dQ+dW

can be shown to be

dQ=(CV/R)*VdP +(Cp/R)*PdV

I have an answer, but am hesitant to say it is a final answer or even the correct one at that.

I will admit that while doing the problem I had trouble following what I was doing. Hence my posting the question. It seemed to me that because we know how state functions act and change with certain processes, that much of the problem is a more of a "plug and chug" approach.

But, I am concerned with the partial derivatives when rearranging this equation. How do certain parts cancel out or how does one approach the problem without them? Is it safe to assume that since you know how the state variables will act in a certain process, that you can use that knowledge to provide a better or more exact answer to the problem?

Attached you will find a picture of the problem that I have done to the best of my ability (which is limited I must say).

If anyone can provide an explanation as to why certain things are done the way they are, or correct my dissection of this problem, I would be grateful for your time in the matter.

What I am looking for in particular, is how do I make my assumptions? Do I assume holding one constant to solve the equation in one way, i.e. adiabatic process, isothermal process, etc. Then do the same for another path and compare?

p.s. The last bit of the problem asked to show how PV^gamma=Constant and can be disregarded.

enter image description here

For class we have been asked to show how the First Law of thermodynamics.

$$\mathrm dU = \mathrm dQ + \mathrm dW$$

can be shown to be

$$\mathrm dQ = \frac{C_V}{R}V\,\mathrm dP + \frac{C_p}{R}P\,\mathrm dV$$

assuming a closed system.

I have an answer, but am hesitant to say it is a final answer or even the correct one at that.

I will admit that while doing the problem I had trouble following what I was doing. Hence my posting the question. It seemed to me that because we know how state functions act and change with certain processes, that much of the problem is a more of a "plug and chug" approach.

But, I am concerned with the partial derivatives when rearranging this equation. How do certain parts cancel out or how does one approach the problem without them? Is it safe to assume that since you know how the state variables will act in a certain process, that you can use that knowledge to provide a better or more exact answer to the problem?

Attached you will find a picture of the problem that I have done to the best of my ability (which is limited I must say).

If anyone can provide an explanation as to why certain things are done the way they are, or correct my dissection of this problem, I would be grateful for your time in the matter.

What I am looking for in particular, is how do I make my assumptions? Do I assume holding one constant to solve the equation in one way, i.e. adiabatic process, isothermal process, etc. Then do the same for another path and compare?

Working for above proof

2 Corrected minor syntax errors. Added homework tag.
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how How to properly rearrange the first law of thermodynamics?

For class we have been asked to show how the first law of thermodynamics.

dU=dQ+dW

can be shown to be

dQ=(CV/R)*VdP +(Cp/R)*PdV

I have an answer, but am hesitant to say it is a final answer or even the correct one at that.

I will admit that while doing the problem I had trouble following what I was doing. Hence my posting the question. It seemed to me that because we know how state functions act and change with certain processes, that much of the problem is a more of a "plug and chug" approach.

But, I am concerned with the partial derivatives when rearranging this equation. How do certain parts cancel out or how does one approach the problem without them? Is it safe to assume that since you know how the state variables will act in a certain process, that you can use that knowledge to provide a better or more exact answer to the problem?

Attached you will find a picture of the problem that I have done to the best of my ability (which is limited I must say).

If anyone can provide an explanation as to why certain things are done the way they are, or correct my dissection of this problem, I would be grateful for your time in the matter.

What I am looking for in particular, is how do I make my assumptions? Do I assume holding one constant to solve the equation in one way, i.e. Adiabaticadiabatic process,isothermal isothermal process, etc. Then do the same for another path and then compare?

p.s. theThe last bit of the problem asked to show how PV^gamma=Constant and can be disregarded

Best Regards,

D .

enter image description here

how to properly rearrange the first law of thermodynamics

For class we have been asked to show how the first law of thermodynamics

dU=dQ+dW

can be shown to be

dQ=(CV/R)*VdP +(Cp/R)*PdV

I have an answer, but am hesitant to say it is a final answer or even the correct one at that.

I will admit that while doing the problem I had trouble following what I was doing. Hence my posting the question. It seemed to me that because we know how state functions act and change with certain processes that much of the problem is a more of a "plug and chug" approach.

But I am concerned with the partial derivatives when rearranging this equation. How do certain parts cancel out or how does one approach the problem without them? Is it safe to assume that since you know how the state variables will act in a certain process that you can use that knowledge to provide a better or more exact answer to the problem?

Attached you will find a picture of the problem that I have done to the best of my ability (which is limited I must say)

If anyone can provide an explanation as to why certain things are done the way they are or correct my dissection of this problem I would be grateful for your time in the matter.

What I am looking for in particular is how do I make my assumptions? Do I assume holding one constant to solve the equation in one way i.e. Adiabatic process,isothermal, etc. Then do the same for another path and then compare?

p.s. the last bit of the problem asked to show how PV^gamma=Constant and can be disregarded

Best Regards,

D

enter image description here

How to properly rearrange the first law of thermodynamics?

For class we have been asked to show how the first law of thermodynamics.

dU=dQ+dW

can be shown to be

dQ=(CV/R)*VdP +(Cp/R)*PdV

I have an answer, but am hesitant to say it is a final answer or even the correct one at that.

I will admit that while doing the problem I had trouble following what I was doing. Hence my posting the question. It seemed to me that because we know how state functions act and change with certain processes, that much of the problem is a more of a "plug and chug" approach.

But, I am concerned with the partial derivatives when rearranging this equation. How do certain parts cancel out or how does one approach the problem without them? Is it safe to assume that since you know how the state variables will act in a certain process, that you can use that knowledge to provide a better or more exact answer to the problem?

Attached you will find a picture of the problem that I have done to the best of my ability (which is limited I must say).

If anyone can provide an explanation as to why certain things are done the way they are, or correct my dissection of this problem, I would be grateful for your time in the matter.

What I am looking for in particular, is how do I make my assumptions? Do I assume holding one constant to solve the equation in one way, i.e. adiabatic process, isothermal process, etc. Then do the same for another path and compare?

p.s. The last bit of the problem asked to show how PV^gamma=Constant and can be disregarded.

enter image description here

1
source | link

how to properly rearrange the first law of thermodynamics

For class we have been asked to show how the first law of thermodynamics

dU=dQ+dW

can be shown to be

dQ=(CV/R)*VdP +(Cp/R)*PdV

I have an answer, but am hesitant to say it is a final answer or even the correct one at that.

I will admit that while doing the problem I had trouble following what I was doing. Hence my posting the question. It seemed to me that because we know how state functions act and change with certain processes that much of the problem is a more of a "plug and chug" approach.

But I am concerned with the partial derivatives when rearranging this equation. How do certain parts cancel out or how does one approach the problem without them? Is it safe to assume that since you know how the state variables will act in a certain process that you can use that knowledge to provide a better or more exact answer to the problem?

Attached you will find a picture of the problem that I have done to the best of my ability (which is limited I must say)

If anyone can provide an explanation as to why certain things are done the way they are or correct my dissection of this problem I would be grateful for your time in the matter.

What I am looking for in particular is how do I make my assumptions? Do I assume holding one constant to solve the equation in one way i.e. Adiabatic process,isothermal, etc. Then do the same for another path and then compare?

p.s. the last bit of the problem asked to show how PV^gamma=Constant and can be disregarded

Best Regards,

D

enter image description here