What is the amount of work done by an ideal gas, if the gas expands isothermally from $10^{-3} ext{ m}^3$ to

Question

What is the amount of work done by an ideal gas, if the gas expands isothermally from $10^{-3} 	ext{ m}^3$ to $10^{-2} 	ext{ m}^3$ at $300 	ext{ K}$ against a constant pressure of $10^5 	ext{ N m}^{-2}$?

Accepted Answer

The work done during an isothermal expansion against a constant external pressure ($p_{ex}$) is given by the formula:
$W = -p_{ex} \Delta V = -p_{ex} (V_f - V_i)$
Given:
External pressure, $p_{ex} = 10^5 	ext{ N m}^{-2}$
Initial volume, $V_i = 10^{-3} 	ext{ m}^3$
Final volume, $V_f = 10^{-2} 	ext{ m}^3$
Substituting the given values into the equation:
$W = -10^5 	ext{ N m}^{-2} 	imes (10^{-2} - 10^{-3}) 	ext{ m}^3$
$W = -10^5 	imes (0.01 - 0.001) 	ext{ J}$
$W = -10^5 	imes 0.009 	ext{ J} = -900 	ext{ J}$.
Thus, the work done by the gas is $-900 	ext{ J}$.

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