If the work done during isothermal reversible expansion of an ideal gas at apressure of 10 atm from 4 lit to a final volume is -184.24,find the final volume of the gas?

To find the final volume of the gas during an isothermal reversible expansion, we can use the formula for work done in such a process. The work done (W) on or by an ideal gas during isothermal expansion can be expressed as:

Work Done in Isothermal Expansion

The formula for work done in an isothermal process is given by:

W = -P_ext * ΔV

Where:

• W = work done (in joules or liters-atm)
• P_ext = external pressure (in atm)
• ΔV = change in volume (final volume - initial volume, in liters)

Given Values

From your question, we have:

• Initial volume (V_i) = 4 liters
• External pressure (P_ext) = 10 atm
• Work done (W) = -184.24 L·atm

Calculating Change in Volume

We can rearrange the work formula to find the change in volume:

ΔV = -W / P_ext

Substituting the known values:

ΔV = -(-184.24) / 10

ΔV = 184.24 / 10 = 18.424 liters

Finding Final Volume

Now that we have the change in volume, we can find the final volume (V_f) using the initial volume:

V_f = V_i + ΔV

Substituting the values:

V_f = 4 liters + 18.424 liters

V_f = 22.424 liters

Final Result

The final volume of the gas after the isothermal reversible expansion is approximately 22.42 liters.