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A cylinder contains (500 g) of helium at (120 atm) and (20°C). The valve is leaky, and all the gas slowly escapes isothermally into the atmosphere. Use the results of the preceding problem to determine the resulting change in entropy of the universe.

a) Calculate the change in entropy of the universe during helium escape.
b) The change in entropy depends on the specific heat of helium.
c) The leaky valve has no effect on the change in entropy.
d) The entropy change is unaffected by the isothermal process.

1 Answer

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Final answer:

The entropy of the universe increases when helium gas escapes from a cylinder into the atmosphere in an isothermal process. Calculations of this increase do not require the specific heat of helium. The leaky valve and the isothermal condition have no effect on the overall change in entropy of the universe.

Step-by-step explanation:

Entropy Change of the Universe

When helium gas escapes isothermally into the atmosphere from a cylinder, we observe an increase in the entropy of the universe. This is due to the fact that the gas expands from an area of high pressure to one of lower pressure (the atmosphere), and during this isothermal process, the temperature remains constant. According to the second law of thermodynamics, entropy, which is a measure of disorder, increases in spontaneous processes such as gas expansion. The change in entropy can be calculated using the formula ΔS = Q/T, where Q is the heat transferred and T is the absolute temperature. In this case, the specific heat of helium is not required since we are considering an isothermal process where temperature remains constant.

The leaky valve, which simply provides a mechanism for the gas to escape, does not affect the overall change in entropy of the helium or the universe. Since the process is carried out isothermally, the temperature of the gas does not change, and thus the change in entropy of the universe is unaffected by the isothermal condition.

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