ThermodynamicsHard
Question
A piston can freely move inside a horizontal cylinder closed from both ends. Initially, the piston separates the inside space of the cylinder into two equal parts each of volume Vo, in which an ideal gas is contained under the same pressure Po and at the same temperature. What work has to be performed in order to increase the volume of one part of gas isothermally $\eta$ times when compared to that of the other by slowly moving the piston?
Options
A.$P_{o}V_{o}\ln\eta$
B.$P_{o}V_{o}\ln\frac{(\eta + 1)^{2}}{4\eta}$
C.$P_{o}V_{o}\ln\frac{(\eta - 1)^{2}}{4\eta}$
D.$2P_{o}V_{o}\ln\eta$
Solution
Work performed on the piston
$= - \left\lbrack \int_{V_{o}}^{\eta V}P_{1}.dV + \int_{V_{0}}^{V}{P_{2}.dV} \right\rbrack\text{ and }(V + \eta.V) = 2V_{0} $$$= P_{0}V_{0}.\ln\frac{(\eta + 1)^{2}}{4\eta}$$
Create a free account to view solution
View Solution FreeMore Thermodynamics Questions
Consider the reaction: N2 + 3H2 → 2NH3 carried out at constant temperature and pressure. If ᐃH and ᐃU ...Five moles of an ideal gas expand isothermally and reversibly from an initial pressure of 100 atm to a final pressure of...For which of the following process, ΔS is negative?...In a certain polytropic process, the volume of argon was increased 4 times. Simultaneously, the pressure decreased 8 tim...For which of the following process ΔS°sys is positive?...