Question

W =-
.
In thermodynamics the P-V work done is given by
--JavPext
For a system undergoing a particular process, the work done is,
RT
a
W =_
:-
fav v bo v
This equation is applicable to a
(A) System that satisfies the van der Waals equation of state.
(B) Process that is reversible and isothermal.
(C) Process that is reversible and adiabatic.
(D) Process that is irreversible and isothermal.

Answer 1

Final answer:  Correct options are,

    (A) system that satisfies the van der Waals equation of state.

    (B) process that is reversible and isothermal.

    (C) process that is reversible and adiabatic.  

Given that: We are given $w = - \int\limits {P_{ext} \, dV$ and  $w = -\int\limits ({\frac{RT}{V-b}-\frac{a}{V^{2} })} \, dV$

To find: We have to find which condition satisfy the given equations.

Explanation:

• Given that, $w = - \int\limits {P_{ext} \, dV$

• For n mole of gas, the van der Waals equation is:

            $(P + \frac{an^{2}}{V^{2}} )(V - nb) = nRT$

Thus, for a van der Waals gas,

           $P = \frac{nRT}{V - nb} - \frac{an^{2} }{V^{2}}$

For 1 mole of gas put n=1

           $P = \frac{RT}{V - b} - \frac{a}{V^{2} }$

• For a reversible process  $P_{ext} = P_{gas}$

           So, $w = - \int\limits {P_{ext} \, dV$

                  $w = -\int\limits ({\frac{RT}{V-b}-\frac{a}{V^{2} })} \, dV$

Hence, van der Waals equation of state satisfy this process.

Option (a) system that satisfies the van der Waals equation of state is correct.

• For a gas expand reversibly $P_{ext} = P_{gas}$

                $P_{gas} = \frac{RT}{V - b} - \frac{a}{V^{2} }$

                $w = -\int\limits ({\frac{RT}{V-b}-\frac{a}{V^{2} })} \, dV$

this equation is applicable to the process that is reversible and isothermal. option (b) process that is reversible and isothermal is also correct.

• For an adiabatic process there is no heat enters or leaves the system. The system is completely insulated from the surroundings. Hence q=0.

For a gas expand reversibly, $P_{ext} = P_{gas}$

There is no heat terms in  $w = -\int\limits ({\frac{RT}{V-b}-\frac{a}{V^{2} })} \, dV$

So, this equation is applicable to option (C) Process that is reversible and adiabatic.

• Consider the irreversible and isothermal process when the external pressure $P_{ext}$ is constant throughout the expansion. Unlike the case of reversible expansion here $P_{ext}$ is significantly smaller than pressure of the gas $P_{gas}$.

So, work done is less than that associated with reversible isothermal expansion. Hence process is not applicable for an irreversible process.

(d) Process that is irreversible and isothermal is wrong answer.

• Correct options are,

(A) system that satisfies the van der Waals equation of state.

(B) process that is reversible and isothermal.

(C) process that is reversible and adiabatic.

To know more about the concept please go through the links

https://brainly.in/question/2724479

https://brainly.in/question/9751178

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