A sample of gas in a cylinder of volume 4.09 L
at 289 K and 3.43 atm expands to 7.73 L
by two different pathways. Path A is an
isothermal, reversible expansion. Calculate
the work
To calculate the work done during the isothermal, reversible expansion (Path A), we can use the formula:
Work (W) = -nRT ln(V2/V1)
where:
- W is the work done
- n is the moles of gas
- R is the gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin (289 K)
- V1 is the initial volume (4.09 L)
- V2 is the final volume (7.73 L)
To use this formula, we need to determine the number of moles of gas (n). We can calculate this using the ideal gas law:
PV = nRT
Rearranging the equation, we get:
n = PV / RT
Substituting the given values:
n = (3.43 atm) * (4.09 L) / (0.0821 L·atm/(mol·K) * 289 K)
n = 0.5967 moles
Now, plugging in the values into the work formula:
W = - (0.5967 moles) * (0.0821 L·atm/(mol·K)) * (289 K) * ln(7.73 L / 4.09 L)
Simplifying the expression and solving the equation:
W = - (0.5967 moles) * (0.0821 L·atm/(mol·K)) * (289 K) * ln(1.888)
W = - (0.5967 moles) * (0.0821 L·atm/(mol·K)) * (289 K) * 0.634
W ≈ -35.99 L·atm