Chemical Engineering Thermodynamics MCQ Questions & Answers | Chemical Engineering

By $$T-Ds$$  Equations at constant entropy
$${C_p}dT = T{\frac{{\partial V}}{{\partial T}}_P}dP$$     and  $${C_v} = - T{\left( {\frac{{\partial P}}{{\partial T}}} \right)_P}{\left( {\frac{{\partial V}}{{\partial T}}} \right)_S}$$
$$ \Rightarrow \frac{{{C_P}}}{{{C_V}}} = \frac{{\left( {\frac{{\partial P}}{{\partial V}}} \right)S}}{{\left( {\frac{{\partial P}}{{\partial V}}} \right)T}}$$
Since, $${C_P}$$ is always greater than $${C_V}$$ the ratio of isothermal compressibility and isentropic (reversible adiabatic) process is always greater than $$1 \Rightarrow $$ the difference is greater than zero.

$$dU = CvdT - \left[ {P + T\left( {\frac{{\left( {\frac{{\partial V}}{{\partial T}}} \right)P}}{{\left( {\frac{{\partial V}}{{\partial P}}} \right)T}}} \right)dV} \right]$$       Since in case of incompressible fluid
$$\eqalign{ & dV = 0 \cr & \Rightarrow dU = {C_V}dT \cr} $$
So, internal energy is a function of temperature only.

$$NTP$$   conditions are $${20^ \circ }C$$  and $$760\,mm\,Hg.$$

Since internal energy of an incompressible fluid is dependent only on temperature $$dH = dU + VdP.$$
Since $$dV = 0$$   for incompressible fluid so, enthalpy of an incompressible fluid is linearly dependent on pressure.

Since for a reversible adiabatic process the entropy is constant.
The heat-capacity and entropy relation is given by
$$\eqalign{ & \frac{{{C_P}}}{T}dT = dS \cr & \Rightarrow {C_P} = 0. \cr} $$

We know for reversible process $$TdS = \delta Q$$   and since in adiabatic process $$\delta Q = 0 \Rightarrow TdS = 0$$     so reversible adiabatic process is an isentropic process.

Activity co-efficient is defined as the ratio of fugacity at existing conditions to fugacity in ideal solution. Since fugacity is a function of temperature, pressure and composition we can say activity co-efficient is also a function of temperature pressure and composition.

Fugacity is nothing but escaping tendency or effective pressure since at lower pressures it will be equal to pressure and at higher pressures as intermolecular forces come to play the fugacity changes from pressure. So, we physically say fugacity is an function of pressure and in an similar way the temperature dependency can also be said. Since higher the composition of a particular component in solution higher is the fugacity or its escaping tendency we can say fugacity is also a function of composition.

Given process is solubility of a particular component in an solution and it is increasing with increase in volume so, physically we can say it decreases with pressure because under decreasing pressure the volume of solution increases and the process is exothermic given. So, by Le Chatelier's principle we can say the process is favored by taking out or decreasing the temperature.

Since the third law of thermodynamics is concern about entropy of a pure crystalline substance at absolute zero temperature this can be used as a reference.