For an ideal gas with initial pressure and volume Pi and Vi, respectively, a reversible isothermal expansion happens, when its volume becomes V0. Then it is compressed to its original volume Vi by a reversible adiabatic process. If the final pressure is Pf, then which of the following statements is true ?

Question

For an ideal gas with initial pressure and volume Pi and Vi, respectively, a reversible isothermal expansion happens, when its volume becomes V0. Then it is compressed to its original volume Vi by a reversible adiabatic process. If the final pressure is Pf, then which of the following statements is true ? (A) Pf = Pi (B) Pf > Pi (C) Pf < Pi (D) (Pf/V0) = (Pi/Vi)

Tardigrade Admin · Accepted Answer

In p -V diagram, the slope of an adiabatic curve at any point in steeper than that of isothermal curve at that point. Thus, pf > pi

$P_{f} = P_{i}$

$P_{f} > P_{i}$

$P_{f} < P_{i}$

$\frac{P _{f}}{V _{0}} = \frac{P _{i}}{V _{i}}$

In $p - V$ diagram, the slope of an adiabatic curve at any point in steeper than that of isothermal curve at that point.
Thus, $p_{f} > p_{i}$

Pf​=Pi​

Pf​>Pi​

Pf​<Pi​

V0​Pf​​=Vi​Pi​​

In p−V diagram, the slope of an adiabatic curve at any point in steeper than that of isothermal curve at that point. Thus, pf​>pi​

$P_{f} = P_{i}$

$P_{f} > P_{i}$

$P_{f} < P_{i}$

$\frac{P _{f}}{V _{0}} = \frac{P _{i}}{V _{i}}$

In $p - V$ diagram, the slope of an adiabatic curve at any point in steeper than that of isothermal curve at that point.
Thus, $p_{f} > p_{i}$