A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here:
Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case (2) the piston is fixed so that it cannot move. (b) Identify the sign (positive, negative, or zero) of q and w in each case?

Question

A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here:

Illustration of a gas cylinder with a piston and heater for thermodynamics study.

Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case (2) the piston is fixed so that it cannot move. (b) Identify the sign (positive, negative, or zero) of q and w in each case?

Accepted Answer

welcome back everyone in this example, We have a chamber with a piston. So the piston here is this T shaped device that is placed inside of our chamber here And this is placed on a hot plate which heats our chamber with a supply of 300 joules of energy. Now we need to determine a two part question here where in part a our piston is being fixed so it just stays tucked into our chamber here and we need to determine what the signs of Q which we should recall represents heat and W which we should recall represents work would be so for Q. Or heat. We should recognize that if our if our piston is fixed in our chamber then all of the 300 jewels of heat energy from our hot plate are going to be able to be transferred to our chamber which has our gas. So just to specify here our system is our gas inside of the chamber and the surroundings would be the outside of the chamber or the environment outside of our chamber which holds our gas. And so we would say that since all of our 300 joules of energy is able to be transferred to the system or to our gas contained within the chamber. We can say that therefore our sign for Q is going to be positive. So our sign for heat should be positive because we would have a net gain of heat to our system. Whereas for our sign of W which stands for work, we recall, we also want to think of work in terms of our system and so our system being, our gas is fixed in the chamber by our piston, which is keeping our gas contained within the chamber. And so because our and we'll use the color red here actually for work. Our piston keeps gas fixed within the chamber. And so we can say that therefore our system being our gas is unable to expand and by expanding, that is the method of our system doing work. And so we would say that therefore are signed for work is going to equal a value of zero because our system being the gas in the chamber is not able to do any work at all, because it's contained within the chamber by the piston and is unable to expand. So for our answers for part A, we have work equal to zero and Q being a positive value. Moving on to part B of the prompt, we are told that the piston is now allowed to move and so now we need to determine what are signs of heat and work will now be so if our piston is allowed to move and I'm just going to scroll down for more room, we can say sorry. So the piston is now unable to keep gas fixed inside the chamber. And so we can say that thus our system being our gas is able to expand to the surroundings or outside of our chamber as we stated above. Until we can say that therefore our system does work on the surroundings by expanding and that means that work is negative. So this would be our first answer for part B of the prompt. And now we need to determine what our sign for heat will be according to prompt B. So right now we answered our symbol for work for part B. Now, as far as heat for part B. If the piston is now allowed to move some of the heat energy will be lost to the surroundings when the gas expands to the surroundings. However, the heat energy that is affecting our system is coming from electrical heat energy from our hot plate. And so we should recall that electrical heat energy transfers inefficiently. And so even though we still might lose some of this heat to our surroundings, we can still have And sorry about that you can say but there is still a net gain of heat transferred to the system being again our gas. And so we would say that therefore our sign for heat is also still going to be positive. And so this statement for part B of our prompt represents our second and last final answer here. So everything highlighted in yellow in our solution represents our final answers as these symbols for heat and work in scenarios A and B. So I hope that everything that I reviewed was clear. If you have any questions please leave them down below and I will see everyone in the next practice video.

Verified Solution

Key Concepts

First Law of Thermodynamics

Heat (q) and Work (w)

System Constraints