Chemical Engineering Thermodynamics MCQ Questions & Answers | Chemical Engineering

For a polytrophic process we know $$P{V^n} = {\text{constant}}$$
So, the work done in an polytrophic process is $$W = \frac{{{P_2}{V_2} - {P_1}{V_1}}}{{n - 1}}$$
So, we can see clearly when $$n = 1$$  the work done is becoming infinity which is wrong conceptually hence the above formulae can’t be applied in case of isothermal $$\left( {n - 1} \right)$$  process.

For a isothermal process since temperature should remains constant and for an ideal gas undergoing reversible isothermal process can $$b$$ represented by $$PV=nRT.$$

We know for an ideal gas the internal energy is given by:
Actually the internal energy (U) of any substance is a function of
$$\eqalign{ & dU = CvdT - \left[ {P + T\left( {\frac{{\left( {\frac{{\partial V}}{{\partial T}}} \right)p}}{{\left( {\frac{{\partial V}}{{\partial P}}} \right)T}}} \right)dV} \right] \cr & {\text{For an ideal gas, }}PV = RT \cr & {\text{So, }}\left( {\frac{{\partial V}}{{\partial T}}} \right)p = \frac{R}{P}\,\,{\text{and }}\left( {\frac{{\partial V}}{{\partial P}}} \right)T = - \frac{{RT}}{{{P^2}}} \cr & {\text{Hence, }}dU = CvdT \cr} $$
So, in case of isothermal process the internal energy remains constant.

If the polytrophic index is equal to ratio of heat capacities $$\left( \gamma \right)$$  than the process is known as reversible adiabatic process which is also called as isentropic process.

Fugacity coefficient is defined as ratio of fugacity of the substance at the prevailing conditions to the fugacity at standard conditions (usually the conditions where the fugacity is known is taken as standard conditions) For ideal gas since fugacity is equal to pressure The ratio becomes equal to 1.
Actually the definition becomes $${\text{fugacity coefficient}} = \frac{{{\text{fugacity of the gas at some condition}}}}{{{\text{fugacity of the gas at standard condition}}}}$$             if the standard conditions are taken as the same conditions in which the ideal gas is present the equation becomes ratio of pressure and hence equal to one.

The heat capacity of the solid, liquid and gases are different and usually the liquid have higher heat capacity than solids as liquids can absorb more heat as the molecules put the energy into both translational and vibrational kinetic energy. Whereas in solids the energy is put only in vibrational energy.

$$P{V^n} = {\text{constant}},$$    if $$n$$ lies between the $$1$$ and $$y\left( {\frac{{{c_p}}}{{{c_v}}}} \right)$$  then the process is known as polytrophic process when $$n = 1$$  it is called isothermal process and when $$n = y$$  it is called as adiabatic process.

Since when $$n = \pm \infty $$   the equation $$P{V^n} = {\text{constant}}$$     is leading to volume $$=$$ constant the process is called as isochoric process on multiplying the power with $$\frac{1}{\infty }$$ we get the equation $$v = {\text{constant}}.$$

An adiabatic process is represented by $$p{v^\gamma } = {\text{constant}}$$    now by replacing the $$p$$ with $$\frac{{nRT}}{v}$$  we get $$T{V^{\gamma - 1}} = {\text{constant}}$$    and by replacing the $$V$$ with $$\frac{{nRT}}{P}$$  we get the equation $${P^{1 - \gamma }}{T^\gamma } = {\text{constant}}.$$

A reversible process is such a process where the system and surroundings must be brought to the initial positions when the system is brought to initial position for that to achieve the system should not contain friction.