(I) Consider a rubber band which behaves such that if you stretch it adiabatically the temperature...

Question

(I) Consider a rubber band which behaves such that if you stretch it adiabatically the temperature will increase. a. When we do this adiabatic stretching does the internal energy increase. decrease, or remain the same? (Show how you derived your conclusion.) b. If Instead we stretch the rubber band Isothermally what will the entropy do? Increase, decrease or stay the same? (Show how you derived your conclusion.)
(2) The fundamental relation in differential form for a magnetic material is = TdS + M.I.44 assuming a constant volume. We are given Curie's law relating CV the magnetization (M) with the magnetic field (H) as M H T a. Derive an expression for the adiabatic change in temperature with respect to the magnetic field. b. Comment on what this is doing and how it might be useful.
(3) Three parts: Use only a few clear sentences and mathematical expressions for each part and if it is helpful you can draw a chart or diagram. a. Provide a phenomenological explanation (physical rather than simply mathematical) for why an ideal gas will not experience the Joule-Thomson (Throttling) process. b. Provide a mathematical explanation as to how a gas that follows this equation of state ( p = RT 1(v— b)) will behave in a Joule-Thomson
process. c. Comment on the conditions necessary for a van der Waals gas to be cooled in a Joule-Thomson process. Give a phenomenological explanation as to why.
(4) Compute the entropy for a typical page of text from our textbook.

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Robert · Accepted Answer

1. Consider a Rubber band which behaves such that if you stretch it adiabatically the temperature will increase 
(a) When we do this adiabatic stretching does the internal energy will increase, decrease or will remains the same. 
Solution 
When the rubber is stretched the molecules of rubber gets taut and no longer to oscillate results in decrease in Kinetic 
Energy of the molecules of Rubber, but since the process is adiabatic this lost amount of Kinetic Energy produces heat 
which will further increases the temperature of the rubber since the heat produces cannot be exchanged through the 
surrounding due to adiabatic condition. 
Internal Energy of a system is a function of temperature only that means it will change according to the change in 
temperature. Hence in case of stretching of Rubber Temperature of the rubber will increase so its Internal Energy will 
also Increase. 
(b) If instead we stretch the rubber isothermally what will the entropy do? Increase, Decrease or stay the same. 
Solution 
In a rubber molecules of rubber are loosely packed because it is elastic. If we stretch it to some extent these loose pieces 
of molecules gets taut and no longer be able to oscillate which results in decrease in Randomness within the rubber in 
stretched conditions. Hence entropy will decrease if we stretch a Rubber from its normal condition because Entropy is a 
measure of Disorder.
2. The fundamental relation in differential form for a magnetic material is dU = TdS + HdM , assuming a constant 
volume.

(I) Consider a rubber band which behaves such that if you stretch it adiabatically the temperature will increase. a. When we do this adiabatic stretching does the internal energy increase. decrease,...

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