An exothermic reaction is to take place in a vessel under co

An exothermic reaction is to take place in a vessel under conditions of constant T and V. The system will decrease its energy by delta U = 50 kJ per mole, and this will be accompanied by an entropy increase of Delta S = 150 J/K per mole. Assuming that DeltaU and Delta S are nearly independent of temperature, what is the threshold temperature below which the reaction will take place spontaneously? What is the maximum work (per mole) that could be extracted if the reaction takes place at room temperature (294 k)?

Solution

According to first law of thermodynamics

dU=TdS-PdV

Here volume is constant. So, dV=0

So dU=TdS

dU=50000J, dS=150J/K. So threshold temperature is 50000/150=333.33 K.

Now If we Take first law of thermodynamics in the form dU=dQ+dW, where dQ=TdS and dW=-PdV (Work which can be extracted), then for room temperature 294 K, dW=dU-TdS=[50000-(150*294)]Joules=50000-44100=5900 Joules. So The maximum work that can be extracted in room temperature from this system is 5900 Joules.