ThermodynamicsHard
Question
One mole of a certain ideal gas is contained under a weightless piston of a vertical cylinder at a temperature T. The space over the piston opens into the atmosphere. What work has to be performed in order to increase the gas volume isothermally under the piston $\eta$ times by slowly raising the piston? The friction of the piston against the cylinder walls is negligibly small.
Options
A.$RT\left( \eta - 1 - \ln\eta \right)$
B.$RT\left( 1 - \eta + \ln\eta \right)$
C.$RT\ln\eta$
D.$- RT\ln\eta$
Solution
$dw = F.dx = \left( P_{0} - P \right)A.dx = \left( P_{0} - P \right).dV $$${\therefore w = \int_{V}^{\eta V}{\left( P_{o} - \frac{nRT}{V} \right)dV} = P_{0}(\eta V - V) - RT.\ln\frac{V\eta}{V} }{P_{0}V(\eta - 1) - RT.\ln\eta = RT\left( \eta - 1 - \ln\eta \right)}$$
Create a free account to view solution
View Solution FreeMore Thermodynamics Questions
Which of the following is not a thermodynamic property of a system?...A cylinder with thermally insulated walls contains an insulated portion which can slide freely. The partition divides th...The molar heat capacity at 25°C should be close to 27 J/K-mol for all of the given elements except...The magnitude of work done by one mole of a Van der Waals gas during its isothermal reversible expansion from volume V1 ...Standard entropy of X2, Y2 and XY2 are 60, 40 and 50 JK-1mol-1, respectively. For the reaction,, ᐃH = - 30 kJ, to ...