A flask contains helium gas at 11 K . The flask is thermally isolated and the ga

Question

A flask contains helium gas at 11 K . The flask is thermally isolated and the gas is allowed to escape slowly through a narrow tube until the pressure within the flask is 0.98 atm and the temperature is 4.2 K. If the gas is ideal, find the initial pressure for the flask to be entirely filled with liquid at the end of the process.

(Use the first law of thermodynamics equation and use the entropy. Assume the entropy of the remaining gas doesn't change. Find the entropy change on cooling and this will give you an equation. Also use the entropy change on liquefying and this also will give you another equation. Combine the two equations with the help with other simple equations and you will find the initial pressure. This problem can be solved with five equations)

(Make use of the fact that the normal boiling point of helium is 4.2K and the latent of helium at 4.2 K is 20 cal/mole and C_v of helium gas is 3 cal/mole. deg)

Explanation / Answer

First law of thermodynamics states that

U=Q+W--- (1)

s=Q/T

Q=sT

U=sT-Pdv since W=-Pdv

U=s(11)-Pdv-----first condition---- (2)

U=s(4.2)-0.98dv-------- (3)

So change in entropy

s(11)-s(4.2)=P-0.98

Cv log (Tf/Ti) =P-0.98------ (4)

3 log (11/4.2)=P-0.98

1.25=P-0.98-------------(5)

P=1.25+0.98

P=2.23 atm

Please do rate my solution with 5 star ratings.!!!

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.