The very large liquefied natural gas storage tank (LNG,which is well insulated). Contains 40000 m3 of pure liquid methane. The boiling point of liquid methane is near 111K at 1 bar. Normally the filled tank is allowed to attain an equilibrium state with the internal pressure held constant. The tank pressure is 1.044 bar. Over the test period, the measured boil-off rate was 4.267*10^4 mol/h. (a) Calculate the heat leak into the tank (J/h). (b) Over the 24-h period where the boil-off vapor averaged 4.267*10^4 mol/h, despite the best intentions of the operators, the tank pressure fell from 1.044 to 1.043 bar. Calculate the heat leak into the tank.
Assume that the 40000 m3 tank is filled with 99% liquid by volume. For methane at 112 K , 1.044 bar. V(vapor) =8.6036*10^-3 (m^3/mol), V(liquid) =0.038*10^-3 (m^3/mol),dV(vapor)/dT=-6.5015*10^-4(m^3/mol K), dV(liquid)/dT=1.309*10^-7(m^3/mol K,H(vapor)=1.27982*10^4 (J/mol), H(liquid)=4.6052*10^3 (J/mol), dH(vapor)/dT=26.8 (J/mol K) , dH(liquid)/dT=55.96 (J/mol K), dP/dT=0.0854 bar/K