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Thermodynamics

Section: Chemistry

Question : 22 of 40

Marks: +1, -0

(p_1,V_1,T_1)

(p_2,V_2,T_2)

The work done on the gas is maximum when it is compressed irreversibly from $(p_2V_2)$ to $(p_1,V_1)$ against constant pressure $(p_1)$
The change in internal energy of the gas is (i) zero, if it is expanded reversibly with $T_1=T_2$ and (ii) positive, if it is expanded reversibly under adiabatic conditions with $T_1 \neq T_2$
If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic.
The work done by the gas is less when it is expanded reversibly from $V_1$ to $V_2$ under adiabaticconditions as compared to that when expanded reversibly from $V_1$ to $V_2$ under isothermal conditions.

Solution:

\text{State-1}\xrightarrow{\text{Expansion}}\text{State-2}

(p_1,V_1,T_1)

(p_2,V_2,T_2)

⇒Work done in reversible compression process is smaller than the work done in irreversible compression process

⇒

\Delta U=0

for reversible isothermal expansion.

\Delta U < 0

for reversible adiabatic expansion.

⇒ For free expansion

q=0,\ w=0

and

\Delta U=0

hence it is simultaneously both isothermal

(\Delta U=0)

as well as adiabatic (q = 0).

⇒ Work done in reversible adiabatic expansion is less than the work done in reversible isothermal expansion as shown in figure

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