ThermodynamicsHard
Question
A gas expands reversibly in a piston cylinder device from V1 to V2, the process being described by PV = a + bV, where P is in Nm–2, V is in m3 and a and b are constants. The work done in the process (w) is
Options
A.$a\log_{e}\left( \frac{V_{1}}{V_{2}} \right) + b\left( V_{2} - V_{1} \right)$
B.$- a\log_{e}\left( \frac{V_{2}}{V_{1}} \right) - b\left( V_{2} - V_{1} \right)$
C.$- a\log_{e}\left( \frac{V_{1}}{V_{2}} \right) - b\left( V_{2} - V_{1} \right)$
D.$a\log_{e}\left( \frac{V_{2}}{V_{1}} \right) + b\left( V_{2} - V_{1} \right)$
Solution
$w = - \int_{V_{1}}^{V_{2}}{P.dv} = - \int_{V_{1}}^{V_{2}}\left( \frac{a}{V} + b \right)dv$
$= - a\ln\frac{V_{2}}{V_{1}} - b\left( V_{2} - V_{1} \right)$
Create a free account to view solution
View Solution FreeMore Thermodynamics Questions
6 mole of an ideal gas expand isothermal and reversibly from a volume of 1 liter to avolume of 10 liters at 27oC. What i...For an isolated system, the wall/boundary separating the system from surrounding must be...For a particular reversible reaction at temperature T, ᐃH and ᐃS were found to be both +ve. If Te is the tem...One mole of an ideal monoatomic gas undergoes adiabatic free expansion from 2 to 20 dm3, 300 K. The value of ΔS for the ...The direct conversion of A to B is difficult, hence it is carried out by the following shown path: Given ᐃS(A U...