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rtareen
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- TL;DR Summary
- A gas is contained in an insulated cylinder with a movable piston onto of which is a lead shot with mass. The thermal reservoir at the bottom allows for heat the be transferred to the gas.
Be organized and specific about what is changing and what isn't and think it through:rtareen said:In this system (consisting of just the gas) heat is transferred to the gas by means of a reservoir. So this means energy is added to the system. Does this necessarily mean that the work done on the lead shot due to an increased pressure will equal the heat that enters the gas? We are assuming everything is ideal. The book does not really say what would happen. How can we know? What dictates how much work the gas will do?
I don't think that matches the problem the OP is trying to solve, nor do I think it is true that that process would be isothermal given that the piston is insulated.kuruman said:I think it is safe to ask what would happen if, starting from equilibrium, you add (or remove) a piece of lead shot and wait until the system reaches equilibrium again. That will be an isothermal compression (or expansion). You can calculate the final pressure from the added weight, then use the ideal gas law to find the final volume and do the integral to find the work done by the gas.
The piston is insulated but in thermal contact with the heat reservoir. As shown in the figure, heat may be exchanged with the reservoir. I would agree, though, that an isothermal process is not necesarily what OP is trying to solve. OP asserts that "heat is transferred to the gas by means of a reservoir". However, there is no mention whether the heat transfer is taking place isothermally, isobarically or in some other manner. I like the isothermal process because it has the simple feature that whatever heat is added to the gas is equal to the work done by the gas on the piston.russ_watters said:I don't think that matches the problem the OP is trying to solve, nor do I think it is true that that process would be isothermal given that the piston is insulated.
kuruman said:The piston is insulated but in thermal contact with the heat reservoir. As shown in the figure, heat may be exchanged with the reservoir. I would agree, though, that an isothermal process is not necesarily what OP is trying to solve. OP asserts that "heat is transferred to the gas by means of a reservoir". However, there is no mention whether the heat transfer is taking place isothermally, isobarically or in some other manner. I like the isothermal process because it has the simple feature that whatever heat is added to the gas is equal to the work done by the gas on the piston.
russ_watters said:Be organized and specific about what is changing and what isn't and think it through:
An answer of "yes" is a change in energy and a "place" where energy is going. You didn't actually develop a clear-cut problem here, so I'm going to assume the unknown you are trying to solve for is how far the cylinder moves, given a fully defined starting state and a given amount of heat addition. Along the way, you account for where the energy goes.
- It is being heated, so is the temperature of the gas changing?
- It is a sealed piston, so is the mass of gas changing?
- The piston moves, so is the volume of gas changing?
- The weight of the bucket of shot isn't changing, so are you sure the pressure is increasing?
What kind of book did that come from and what is the context behind this? It feels like it should be part of a chapter in a thermodynamics book, on constant pressure heat addition:
https://en.wikipedia.org/wiki/Isobaric_process
I do not see how it can be isothermal in the OP's scenario.kuruman said:However, there is no mention whether the heat transfer is taking place isothermally, isobarically or in some other manner. I like the isothermal process because it has the simple feature that whatever heat is added to the gas is equal to the work done by the gas on the piston.
[emphasis mine]rtareen said:Does this necessarily mean that the work done on the lead shot due to an increased pressure will equal the heat that enters the gas?
jbriggs444 said:I do not see how it can be isothermal in the OP's scenario.
For slow changes (negligible acceleration), the pressure in the cylinder is constant due to the piston with the lead shot. So, by inspection we have an isobaric expansion.
If we are pumping in heat and keeping pressure constant, volume will increase and temperature must rise.
I've edited some additional verbiage into the prior post which may be useful.rtareen said:Great! So what does this mean in terms of energy? Does the gas keep the added energy or will it exit the gas by doing work on the lead mass?
jbriggs444 said:I've edited some additional verbiage into the prior post which may be useful.
To directly answer the question: Why can't it be a little of both?
jbriggs444 said:For slow changes (negligible acceleration), the pressure in the cylinder is constant due to the piston with the lead shot. So, by inspection we have an isobaric expansion.
As long as the gas expands, the work ##W## done by the gas is positive. The first law of thermodynamics always holds true. To figure out whether the heat added to the gas is greater than or less than the work done by the gas, we need to know how this heat is added. If it is added at constant temperature, the work done by the gas is equal to the heat added so no net change in the internal energy. That's the dividing line. If heat is added at constant pressure, more heat enters the gas than work leaves it so there is a net increase in the internal energy. If less than the isothermal amount of heat enters the gas while the gas expands, then the internal energy will decrease.rtareen said:You say that the gas will do work as the knob turn up. The pressure increases, and this translates to energy leaving the gas through work. Then when we stop turning the knob the piston slowly comes to a stop. So I think you're implying that the gas does an amount of work proportional to the amount of heat added. So you answered part of the question, whether there will be work. But you didn't explicitly say whether this work will be equal to the amount of energy gained by the gas through heat transfer. In other words
##\Delta E_{int} = Q - W = 0##?
The principle of energy conservation states that energy cannot be created or destroyed, but can only be transformed from one form to another.
To determine if the energy of a system is conserved, you must calculate the total energy of the system at different points in time and see if it remains constant. If the total energy remains the same, then the energy of the system is conserved.
The conservation of energy in a system can be affected by external forces, such as friction or air resistance, as well as internal forces, such as energy being converted from one form to another within the system.
No, the energy of a closed system, where there is no exchange of energy with the surroundings, cannot change. This is because the total energy of a closed system is always conserved.
The law of energy conservation is a fundamental principle in thermodynamics, which is the study of energy and its transformations. It is the first law of thermodynamics and states that the total energy of an isolated system remains constant. This is closely related to the first and second laws of thermodynamics, which describe the transfer and transformation of energy in a system.