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10 grams of hydrogen (an a-ideal diatomic gas) are initially confined to the lef

ID: 2064458 • Letter: 1

Question

10 grams of hydrogen (an a-ideal diatomic gas) are initially confined to the left half of a 30-liter insulated container. The initial temperature is 280 K. The partition separating left and right is then quickly removed, and the gas then expands to fill the container.

How large is the change ?S of the entropy of the gas?

(a) ?S = 0
(b) ?S = +8.75 J/K
(c) ?S = +83.0 J/K
(d) ?S = +59.6 J/K
(e) ?S = +28.8 J/K




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QUESTION 18**
What is the final temperature Tf of the gas?
(a) Tf = 280 K
(b) Tf = 198 K
(c) Tf = 140 K




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QUESTION 19**
Which one of the choices below is correct? A system evolving toward thermal equilibrium
(a) is evolving toward the most likely macrostate.
(b) is evolving toward the most likely microstate.
(c) must be sharing energy or volume with other systems.

Explanation / Answer

first, there are

          10 grams * (1 mol / 2 grams) = 5 mol of gas

Then

deltaS = nR ln(final V / initial V) = 5*8.314 * ln(2) =

             = 28.8 J/K

18) ASSUMING that the vacant half of the container was initially a vacuum (it should have been... i.e. there was no gas in it) the internal energy of the hydrogen gas remains the same when it expands. The temperature of a gas is directly related to the internal energy. Therefore... the temperature does not change. It remains at 280 K.

19) The answer should be (a). A macrostate is defined by macroscopic parameters, such as volume, temperature, pressure, energy, entropy. Thermal equilibrium is defined by these macro parameters.

In contrast, the "most likely" microstate is non-sensical. There could be thousands, even billions, of microstates for which a system could have equal probability.