Final answer:
To calculate the work done by the gas during isothermal expansion, we use the formula W = P1·V1 · ln(V2/V1) after converting the given units to standard units. The work done by the gas can then be found by plugging in the converted values into the equation.
Step-by-step explanation:
The student's question pertains to finding out the work done by an ideal gas during an isothermal expansion. Since the gas is expanding isothermally and performing work on a piston in a sealed cylinder, we need to calculate the work done (W) using the formula: W = nRT · ln(V2/V1), where n is the number of moles of the gas, R is the ideal gas constant, T is the temperature in Kelvin, and V1 and V2 are the initial and final volumes, respectively.
However, we do not have the number of moles (n) or the temperature (T) provided directly, hence we cannot use this formula as is. Instead, for an isothermal process, the work done can also be calculated by the formula W = P1·V1 · ln(V2/V1), where P1 is the initial pressure. Converting the given pressures from ATM to Pa and the volumes from cm³ to m³, we can substitute the values into the formula.
The calculation becomes W = (7.20 atm × 101325 Pa/atm × 8.5 × 10³ cm³ × 10⁻⁶ m³/cm³) · ln((1.8 × 10⁴ cm³ × 10⁻⁶ m³/cm³) / (8.5 × 10³ cm³ × 10⁻⁶ m³/cm³)). After calculating the natural logarithm and the rest of the expression, we find the work done by the gas on the piston.