Question

Two moles of an ideal gas at $ 2{\text{ }}bar $ and $ 27^\circ C $ expand isothermally against a constant pressure of $ \;1bar $ . What is the work done by the gas?

Answer 1

Hint: An isolated system does not interact with the surrounding. When the system is at the minimum energy level then it is a stable equilibrium. The equilibrium has both forward and reverse reactions.

Complete Step By Step Answer:
Three equilibrium states are available; they are chemical equilibrium, thermal equilibrium, and mechanical equilibrium.
If the temperatures of the two systems are equal then the system is said to be a thermal equilibrium.
If the pressure of the two systems is equal then the system is said to be a mechanical equilibrium.
When there is no difference in the temperature, pressure, or chemical potential then the system is said to be a thermodynamic equilibrium system
We know that ideal gas and isothermal,
 $ {P_1}{V_1} = {P_2}{V_2} $
Here,
 $ \dfrac{{{V_2}}}{{{V_1}}} = \dfrac{{{P_1}}}{{{P_2}}} $
Here, the equation is,
 $ W = nRT\left[ {\ln \left( {\dfrac{{{P_1}}}{{{P_2}}}} \right)} \right] $
Given that,
 $ n = 2 $
 $ {P_1} = 2bar $
 $ {P_2} = 1bar $
 $ R = 8.314J/gmolK $
 $ T = 27^\circ C $
Now apply the given data in the above equation,
 $ W = 2 \times 8.314 \times 300 \times \left[ {\ln \left( {\dfrac{2}{1}} \right)} \right] $
Now solve the above equation we can get the work done by gas,
 $ W = 4.988 \times 0.6933 = 3456.96J $
Here, work is
 $ W \approx 3.5KJ $
Work done is, $ 3.5KJ $
Finally, the correct answer is $ 3.5KJ $
When the gas is compressed the positive work is done. And when the gas is expanded then the negative work is done. When the gas volume is fixed zero percent work is done.
When we move an object against the force the work is done.

Note:
The expansion of gases helps to rotatory motion in the rail engine.
The gas expansion is also used in the hot air balloon. The gas can do expansion work or compression work
The system's energy gets changed because of the work and some energy transfer functions like heat.