hw2solv4

# hw2solv4 - Homework#2 Solutions Question 1 Adiabatic...

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Unformatted text preview: Homework #2 Solutions Question 1) Adiabatic Process for an ideal gas. We are given: Δ U = Q + U U = f 2 Nk B T Adiabatic Process means: Q = 0. Hence, from the lst Law, Δ U = W And compressive work can be written as W =- P Δ V . With the above information: f 2 Nk B Δ T =- P Δ V Now use the ideal gas Law PV = Nk B T to eliminate Pressure P, f 2 Nk B Δ T =- Nk B T V Δ V Divide both sides by T , f 2 Δ T T =- Δ V V Integrate both sides from the initial state ( T i ,V i ) to the final state ( T f ,V f ): f 2 Z T f T i dT T =- Z V f V i dV V f 2 ln T f T i =- ln V f V i After exponentiating both sides of the equation, ( T f T i ) f 2 = V i V f Multiply both sides by V f T i f 2 , then V f T f f 2 = V i T i f 2 So, in the other words, V T f 2 = C where C is a constant. Now, we can use the ideal gas law to eliminate T in favor of P: V ( PV Nk B ) f 2 = C 1 Both N and k B are constant, so we can write P f 2 V f 2 +1 = C Where C is another constant. Now raise both sides to the power 2 /f to get PV 2 f (1+ f 2 ) = C 00 and C 00 is also a constant....
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hw2solv4 - Homework#2 Solutions Question 1 Adiabatic...

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