ThermodynamicsHard
Question
One mole of an ideal gas undergoes a reversible process in which the entropy of the gas changes with absolute temperature T as S = aT + Cv,m lnT, where a is a positive constant. If T = To at V = Vo, then the volume dependence of the gas on temperature in this process is
Options
A.T = To + ln V
B.$T = T_{o} + \frac{R}{a}.\ln\frac{V_{o}}{V}$
C.$T = T_{o} + \frac{R}{a}.\ln\frac{V}{V_{o}}$
D.$V = V_{o} + \frac{a}{R}.\ln\frac{T}{T_{o}}$
Solution
$dS = C_{V,m}.\frac{dT}{T} + P.\frac{dV}{T} = a.dT + C_{V,m}.\frac{1}{T}.dT$
$\text{Or, }\int_{V_{o}}^{V}{\frac{R}{V}.dV} = a.\int_{T_{o}}^{T}{dT} \Rightarrow R.\ln\frac{V}{V_{0}} = a\left( T - T_{0} \right) $$$\therefore T = T_{0} + \frac{R}{a}.\ln\frac{V}{V_{0}}$$
Create a free account to view solution
View Solution FreeMore Thermodynamics Questions
An ideal gas undergoes isothermal expansion from (10 atm, 1 L) to (1 atm, 10 L) either by path–I (infinite stage expansi...A diatomic ideal gas initially at 273 K is given 100 cal heat due to which system did 210 J work. The molar heat capacit...If an endothermic reaction is non - spantaneous at freezing point of water and becomes feasible at its boiling point, th...Assuming that water vapour is an ideal gas, the internal energy (ᐃU) when 1 mol of water is vapourised at 1 bar pr...An isolated system comprises of the liquid in equilibrium with vapours. At this stage, the molar entropy of the vapour i...