Chemical Engineering Thermodynamics MCQ Questions & Answers | Chemical Engineering

Water is generally used as a refrigerant fluid in jet refrigerators.

According to Le Chatelier's principle when we apply high pressure the system will react in such a way that it counters the effect of increasing pressure so, the system has to shift the equilibrium towards less number of moles side(thereby, decreasing the volume) and thus opposing the effect. But in the given reaction the numbers of moles are same in both reactants and products side so, the tendency to shift the equilibrium towards products side and reactants side become equal and thus showing no effect on equilibrium.

Given, number of phases $$\left( \emptyset \right) = 3$$
Number of non-reacting components $$= 3$$
So, degree of freedom $$ = C - \emptyset + 2 = 3 - 3 + 2 = 2$$

The Gibbs–Duhem equation is given as $$\sum {} _{i\, = \,1}^n\,\,{n_i}d{\mu _i} = + vdP - sdT$$     at constant temperature and pressure it simply becomes $$\sum {} _{i\, = \,1}^n\,\,{n_i}d{\mu _i} = 0,$$    which tells us that the chemical potential of an specie is not entirely independent on chemical potential of other species and also relates chemical potential with composition if we write this in terms of fugacity and activity co-efficients it will relate them with composition to.

Both the chemical potential and fugacity must be same in all the phases to attain thermodynamic equilibrium. Actually, the calculation of chemical potential and visualizing it physically is slightly tedious so, we introduced the concept of fugacity which is easy to visualize and we have also many correlations to measure it so, the origin of fugacity taken place. And we related the chemical potential with it as following:
$${\mu _i} = RTdln{f_i}$$
So, the equality of chemical potential will result in equality of fugacity also between the phases.

The chemical potential is nothing but partial molar gibbs free energy (since the partial molar functions depicted the change in total molar property with change in composition(moles) we consider partial molar functions as intensive properties), $${\mu _i} = \left( {\frac{{\partial nG}}{{\partial {n_i}}}} \right)T,P,{n_j}$$     when there is only one component ,G(total molar gibbs free energy) becomes independent of composition(intensive property ) so the equation becomes $${\mu _i} = G\left( {\frac{{\partial {n_I}}}{{\partial {n_i}}}} \right)T,P,{n_j}$$
Hence, $${\mu _i} = G$$

One ton of refrigeration is defined as the amount of heat to be extracted from one ton of water at $${0^ \circ }C$$   to convert it to one ton of ice at $${0^ \circ }C.$$  Which is equivalent to heat removal of $$200\,BTU/\min .$$

Internal energy of an ideal gas is solely dependent on temperature and given by the relation: The internal energy of an substance is given by
$$\eqalign{ & dU = CvdT - \left[ {P + T\left( {\frac{{\left( {\frac{{\partial V}}{{\partial T}}} \right)p}}{{\left( {\frac{{\partial V}}{{\partial P}}} \right)T}}} \right)dV} \right] \cr & {\text{For an ideal gas, }}PV = RT \cr & {\text{So, }}\left( {\frac{{\partial V}}{{\partial T}}} \right)p = \frac{R}{P}\,\,{\text{and }}\left( {\frac{{\partial V}}{{\partial P}}} \right)T = - \frac{{RT}}{{{P^2}}} \cr & {\text{Hence, }}dU = CvdT \cr} $$
So internal energy is only a function of temperature and increases with increase in temperature.

All the given statements are correct. According to Le Chatelier's principle when we apply high pressure the system will react in such a way that it counters the effect of increasing pressure so, the system has to shift the equilibrium towards less number of moles side(thereby, decreasing the volume) and thus opposing the effect. But in the given reaction the numbers of moles are same in both reactants and products side so, the tendency to shift the equilibrium towards products side and reactants side become equal and thus showing no effect on equilibrium.