Question

The system consists of reactants (10.5 g of butane gas and the stoichiometric amount of oxygen gas) placed in a diathermic cylinder sealed from the surroundings by a diathermic, freely moving, massless piston. The cylinder is placed in a huge water tank at 300.K. In the initial state, the system is in equilibrium with the surroundings at 300.K and 1.0 atm. As a result of the combustion between the reactants, the system reaches a final state that contains only carbon dioxide gas and liquid water (i.e. the combustion reaction is assumed to have reached completion). In the final state, the temperature is still 300.K and the pressure is still 1.0 atm. Hence, the process is isothermal and isobaric. The balanced combustion reaction is written as:

C4H10 (g) + 13/2 O2 (g)à4 CO2(g) + 5 H2O(l)

Calculate the expansion/compression work, w, the heat, q, the change in energy, ΔRU, and the change in enthalpy, ΔRH, associated with the combustion of 10.5 g of butane. Hints: Assume ideal gas behavior for butane, oxygen and carbon dioxide and neglect the volume of water liquid in the calculations. Indicate whether the combustion process is an expansion or a compression and make sure the sign of the work is consistent with that observation.

Answer 1

we know that cylinder is diathermic that's why we see that

W = RT*ln (v₂/v₁) so here in this case W= RTln(V/V/2)+RTln(V/2V) which will be equal to RT(ln(2)-ln(2)) = 0 so here what we get that from first law of theremodynamics

Q= u +w so chnage in q = change in U + change in W that will be equal to change in U more over as we know that from ideal gas relationship pv = RT so u will also be zero as T₁ = T₂ but there will be heat because of motion of cylinder which will be calculated by using force balance F = mg/A + F_G