Is point b or c the highest temperature in a PV diagram cycle?

[metaphysicist]

URGENT PHYSIC PROBLEM+Thermodynamic Experts ONLY

go to http://www.xmission.com/~dmcguire/IBPhysics/Units/ThermalPhysics/ThermalPhysicsPracticeTest2004.pdf

solve problem number 28.

is the answer b or c?

argument for b: b is the point of the highest pressure, and lowest volume in the process, it should produce the highest temperature.

argument for c: applying the fact that in a PV diagram, the product of P*V (x and y-coordinate) is nRT (according to the ideal gas law), since nR is constant in the cyclic process, then highest temperature point is found by comparing the P*V at point b and at point c. P*V at point b is 3, and P*V at point c is 9, then by this method point c produce the highest temperature.


So the question is that whether Ideal Gas Law is applicable in this case?

 

[Arctic Fox]

b) B

 

[Clausius2]

At first sight I would say C) or D).

Point C): $$nRT_{c}=9P_oV_o$$

Point D) $$nRT_{d}=8P_oV_o$$

Point B) $$nRT_{b}=3P_oV_o$$

It is clear enough that the highest temperature is at point C). You should not be needed to do any calculations. One can see it at first sight if you know what is an insothermal (T=cte). Such a curve is an hyperbola P=const./V which has the same temperature. That temperature grows at the curve is displaced towards the right of the diagram. Due to the fact that C) is the farthest and highest point, C) has the highest temperature.

You don't need an expert to solve this.

 

[fiber]

the key to IB physics problems is to understant where the equations come from. with this the questions become a lot easier. personally I'm in AP physics but there are some IB'ers in my class.

cheers

-fiber

 

[Andrew Mason]

argument for b: b is the point of the highest pressure, and lowest volume in the process, it should produce the highest temperature.

This would be the correct answer if the system was simply allowed to expand adiabatically from this point (no heat exchanged with surroundings). But if that were to occur, the pressure would drop and you would end up at a pressure well below C. So we can conclude that from B to C, heat is being added to the system - more heat energy than the work done by the gas, since the internal energy (PV = volume x energy/unit volume) of the gas increases. Therefore temperature (PV=nRT) increases.

AM