The pressure and volume of an ideal monatomic gas change from A to B to C, as the drawing shows. The curved line between A and C is an isotherm.
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a)Determine the total heat for the process in joules.
b)State whether the flow of heat is into or out of the gas.
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What do you think? I can help you. I just want to know what you already have. :)
All my best,
Dr. Anna
Thanks for the response.
I wish I had something to go off of. I'm thinking the equation dU=dQ-W has something to do with figuring this out. I'm just unsure where and when to plug things in.
To determine the total heat for the process, we can use the First Law of Thermodynamics, which states that the change in internal energy (∆U) of a system is equal to the heat transferred to the system (Q) minus the work done by the system (W). Mathematically, this can be represented as:
∆U = Q - W
In this case, the process is represented by the curved line between points A and C, which is an isotherm. An isotherm indicates that the temperature remains constant during this process. As a result, the change in internal energy (∆U) would be zero, as there is no change in temperature.
Therefore, the equation can be rewritten as:
0 = Q - W
To find the total heat for the process (Q), we need to determine the work done by the system (W). Since the process is represented by a curved line on the graph, the work done would be given by the area under the curve.
To calculate the work, we can divide the process into two parts: the first part from A to B, and the second part from B to C.
a) Work from A to B: The work done in this part is given by the equation:
W1 = -P∆V
where P is the pressure and ∆V is the change in volume. On the graph, the change in volume ∆V from A to B can be calculated as the difference in volume between the two points. Similarly, the pressure at point A can be read from the graph.
b) Work from B to C: Similarly, the work done in this part is given by the equation:
W2 = -P∆V
where P is the pressure and ∆V is the change in volume. On the graph, the change in volume ∆V from B to C can be calculated as the difference in volume between the two points. Similarly, the pressure at point C can be read from the graph.
To find the total work (W), we sum up the work done in each part:
W = W1 + W2
Finally, since ∆U = 0, we can now substitute the values of W and solve for Q:
0 = Q - (W1 + W2)
Q = W1 + W2
b) To determine whether the flow of heat is into or out of the gas, we need to consider the sign of Q. If Q is positive, it means heat is flowing into the gas, and if Q is negative, it means heat is flowing out of the gas. You can determine the sign by comparing the magnitude of W1 and W2 and the signs of the pressure and volume changes at each step in the process.