Find the work done by 2.32 moles of an ideal gas if its volume doubles at a constant temperature of 22.6°C.
To find the work done by the ideal gas, we can use the following equation:
Work (W) = -PΔV
Where:
- P is the pressure of the gas.
- ΔV is the change in volume of the gas.
Since the pressure and the temperature remain constant, the equation simplifies to:
Work (W) = -PΔV
To find the value of ΔV, we need to know the initial volume (V1) and the final volume (V2). In this case, we know that the volume doubles, so the final volume (V2) is 2 times the initial volume (V1).
To calculate ΔV, we subtract the initial volume from the final volume:
ΔV = V2 - V1
Now, we need the values of the pressure (P), initial volume (V1), and temperature (T) to calculate the work done.
Let's assume the pressure (P) is given or can be found in the problem statement.
Next, to find the initial volume (V1) and convert it into liters, we can divide the given number of moles by Avogadro's number (6.022 x 10^23) and then multiply by the molar volume of an ideal gas at STP (22.4 L/mol).
V1 = (2.32 moles / 6.022 x 10^23) x 22.4 L/mol
Finally, to solve for work (W), substitute the calculated values into the equation:
Work (W) = -PΔV
Note: The temperature given (22.6°C) is not used in this calculation since we assume the temperature remains constant.