Convention of Work in Thermodynamics

In summary, the conventions for positive and negative work done by gas and external forces are based on two different statements of the First Law of Thermodynamics. When considering work done ON the gas, it is negative when the gas expands and positive when it is compressed. However, when considering work done BY the gas, it is positive when the gas expands and negative when it is compressed. This can lead to confusion and it is important to clearly define which statement is being used in a given scenario.
  • #1
Lapetude
3
0

Homework Statement



I am wondering about the following conventions:

The work done by the gas is positive if the gas expands,
and negative if it is compressed.
Conversely, the work done on the gas by external force
(e.g., a moving piston) is positive for compression, and negative when the gas expands.

Why is $$ W_{A,B}=-\int_{A}^{B}PdV $$
Specifically the signs are driving me nuts in working out the total work done on the gas in the Carnot cycle.


Homework Equations



So if a piston is compressing the work done on the gas is by convention positive. But $$dV$$ is negative. So is the negative sign in $$ W_{A,B}=-\int_{A}^{B}PdV $$
a result of trying to make sure the work done is positive in compression?.

The Attempt at a Solution



Consider the Carnot cycle 1st stage of :
isothermal expansion from volume $$V_{1}$$ to volume $$V_{2}$$ at constant temperature $$T_{1}$$. If I use the above definition I get:
$$W=-\int_{V_{1}}^{V{2}}PdV=nRT_{1}Log\left(\frac{V_{1}}{V_{2}}\right)$$
However in this case $$dV$$ is positive so do I just drop the minus from the integral? And hence is the true answer:
$$W=\int_{V_{1}}^{V{2}}PdV=nRT_{1}Log\left(\frac{V_{2}}{V_{1}}\right)$$
which makes no sense if we define the work on a gas as it expands as negative. ie, the above Log will always be positive. If my first answer is correct this would imply that the total work on the gas in the Carnot cycle is negative, while the work done by the gas is positive. Surely this makes sense as we are converting heat into the external work? Thanks in advance.
 
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  • #2
Sorry I just found
https://www.physicsforums.com/showthread.php?t=306228
which is what I'm after.
fysics4fun made it clear:
"mpkannan makes it clear- you must look at everything in context before deciding the signs on everything. A question like "what is the sign on work" is too vague.

Two statements of the First Law of Thermo seen in textbooks:

dU = Q + W and dU = Q - W

W in the first statement is "work on the gas"
W in the second statement is "work by the gas"

And so, for example, when a gas expands W would be negative in the first statement (work done on the gas is negative since positive work is being done on the surroundings).
BUT
when a gas expands W would be positive in the second statement (work done by the gas is positive since work is being done on the surroundings).

The fact that work is negative in one case but positive in the other (both for the same scenario) is not a contradiction, since in one case we're talking about work ON and in the other we're talking about work BY. Textbooks should present BOTH statements of this first law, CLEARLY defining that the first statement is work ON and the second is work BY, in my opinion."
 
  • #3
Lapetude said:
Sorry I just found
https://www.physicsforums.com/showthread.php?t=306228
which is what I'm after.
fysics4fun made it clear:
"mpkannan makes it clear- you must look at everything in context before deciding the signs on everything. A question like "what is the sign on work" is too vague.

Two statements of the First Law of Thermo seen in textbooks:

dU = Q + W and dU = Q - W

W in the first statement is "work on the gas"
W in the second statement is "work by the gas"

And so, for example, when a gas expands W would be negative in the first statement (work done on the gas is negative since positive work is being done on the surroundings).
BUT
when a gas expands W would be positive in the second statement (work done by the gas is positive since work is being done on the surroundings).

The fact that work is negative in one case but positive in the other (both for the same scenario) is not a contradiction, since in one case we're talking about work ON and in the other we're talking about work BY. Textbooks should present BOTH statements of this first law, CLEARLY defining that the first statement is work ON and the second is work BY, in my opinion."
I think everyone feels pretty much the same way.
 

What is the Convention of Work in Thermodynamics?

The Convention of Work in Thermodynamics is a fundamental principle that states that any work done on a system is considered positive, while any work done by a system is considered negative. This convention is essential in understanding the energy transfers in thermodynamic processes.

How is work related to thermodynamics?

Work is a form of energy transfer that is closely related to thermodynamics. In thermodynamics, work is defined as the energy transfer that occurs when a force acts on a system and causes a displacement. This can be seen in processes such as gas expansion or compression, where work is done on or by the system.

Why is the Convention of Work important in thermodynamics?

The Convention of Work is crucial in thermodynamics because it helps us determine the direction of energy transfer in a process. By considering work as either positive or negative, we can accurately calculate the total energy change in a system. This convention also helps us understand the relationship between work and other thermodynamic quantities, such as heat and internal energy.

Can the Convention of Work be violated?

No, the Convention of Work is a fundamental principle in thermodynamics and cannot be violated. It is based on the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred. Therefore, the convention of work must always be followed to ensure energy conservation.

How is the Convention of Work used in thermodynamic calculations?

The Convention of Work is used in various thermodynamic calculations, such as determining the work done in a process, calculating the change in internal energy, and finding the efficiency of a heat engine. By considering work as either positive or negative, we can accurately determine the total energy transfer in a system and make accurate predictions about its behavior.

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