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
The following reaction is performed at 298 K. 2NO(g) + O2(g) ⇋ 2NO2(g) The standard free energy of formation of NO...Molar heat capacity of CD2O (deuterated form of formaldehyde) vapour at constant pressure is vapour 14 cal/K-mol. The en...When a solid melts reversibly...A system is said to be in thermodynamic equilibrium with the surroundings, if...Oxygen gas weighing 64 g is expanded from 1 atm to 0.25 atm at 30°C. What is the entropy change, assuming the gas to be ...