One mole of an ideal monoatomic gas initially at and undergoes a reversible isothermal expansion unt — Thermodynamics and Thermochemistry Chemistry Question
Question
One mole of an ideal monoatomic gas initially at $300 \text{ K}$ and $1 \text{ atm}$ undergoes a reversible isothermal expansion until its final pressure drops to $0.1 \text{ atm}$. Given that the system absorbs heat from the surroundings, calculate the magnitude of the work done by the gas in Joules. (Use $R = 8.314 \text{ J mol}^{-1} \text{ K}^{-1}$, and assume $\ln 10 = 2.303$)
💡 Solution & Explanation
In a reversible isothermal expansion, the mechanical work done *on* the gas follows the formula $w = -nRT \ln(\frac{P_1}{P_2}) = -2.303 nRT \log(\frac{P_1}{P_2})$. Substituting parameters: $w = -2.303 \times 1 \times 8.314 \times 300 \times \log(\frac{1}{0.1}) = -2.303 \times 8.314 \times 300 \times \log(10) = -2.303 \times 2494.2 = -5744.14 \text{ J}$. Work done *by* the gas expands against the surroundings and is expressed as a positive magnitude, which rounds to $5744 \text{ J}$.