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Jacobpm64
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So, I'm a mathematics major about to start my third year. I decided to pick up a physics minor (I've only had the first general physics (mechanics) so far).
Anyway, I'm taking thermodynamics in the fall, so I decided to try to get a heads up on it with some self-study.
If anyone has the Callen book (Thermodynamics and an Introduction to Thermostatistics), I'm on page 21-22.
Example 1 says:
A particular gas is enclosed in a cylinder with a moveable piston. It is observed that if the walls are adiabatic, a quasi-static increase in volume results in a decrease in pressure according to the equation
[tex]P^3 V^5 = [/tex] constant for Q = 0.
a) Find the quasi-static work done on the system and the net heat transfer to the system in each of the three processes (ADB, ACB, and the direct linear process AB) as shown in the figure. (I put the figure as an attachment).
When the author showed how to work out part a, I am confused at a certain part.
His solution says:
Given the equation of the "adiabat" What is this? I'm guessing the equation given in the question. (for which Q = 0 and [tex] \Delta U = W [/tex] ), we find
[tex] U_B - U_A = W_{AB} = -\int_{V_A}^{V_B}PdV = -P_{A}\int_{V_A}^{V_B}\left(\frac{V_A}{V}\right)^{\frac{5}{3}}dV [/tex]
I do not understand how you get from the 2nd to last step to the last step.
Can anyone explain this?
I also did not understand the little explanation about "imperfect differentials" on page 20. (I've had multivariable calculus, but we only spoke of differentials)
Thanks in advance.
Anyway, I'm taking thermodynamics in the fall, so I decided to try to get a heads up on it with some self-study.
If anyone has the Callen book (Thermodynamics and an Introduction to Thermostatistics), I'm on page 21-22.
Example 1 says:
A particular gas is enclosed in a cylinder with a moveable piston. It is observed that if the walls are adiabatic, a quasi-static increase in volume results in a decrease in pressure according to the equation
[tex]P^3 V^5 = [/tex] constant for Q = 0.
a) Find the quasi-static work done on the system and the net heat transfer to the system in each of the three processes (ADB, ACB, and the direct linear process AB) as shown in the figure. (I put the figure as an attachment).
When the author showed how to work out part a, I am confused at a certain part.
His solution says:
Given the equation of the "adiabat" What is this? I'm guessing the equation given in the question. (for which Q = 0 and [tex] \Delta U = W [/tex] ), we find
[tex] U_B - U_A = W_{AB} = -\int_{V_A}^{V_B}PdV = -P_{A}\int_{V_A}^{V_B}\left(\frac{V_A}{V}\right)^{\frac{5}{3}}dV [/tex]
I do not understand how you get from the 2nd to last step to the last step.
Can anyone explain this?
I also did not understand the little explanation about "imperfect differentials" on page 20. (I've had multivariable calculus, but we only spoke of differentials)
Thanks in advance.