What will be the amount of work done in increasing the volume of 10 mols of an ideal gas from one litre to 20 litre at 0C?
W = ν•R•T•ln(V2/V1) =
=10•8.31•273•ln(20/1) = 6.845•10^4 J.
Thankyou Elena
To calculate the amount of work done in increasing the volume of a gas, we can use the formula:
Work = -PΔV
where:
- Work is the amount of work done on the gas (in joules, J)
- P is the pressure of the gas (in pascals, Pa)
- ΔV is the change in volume of the gas (in cubic meters, m³)
In this case, we are given the following information:
- Number of moles (n): 10 mols
- Initial volume (V1): 1 litre (1 L = 0.001 m³)
- Final volume (V2): 20 litres (20 L = 0.02 m³)
- Temperature (T): 0°C = 273.15 K
First, we need to convert the initial and final volumes to cubic meters:
- V1 = 1 L = 0.001 m³
- V2 = 20 L = 0.02 m³
Next, we need to calculate the change in volume:
- ΔV = V2 - V1 = 0.02 m³ - 0.001 m³ = 0.019 m³
Now, we can calculate the work done:
- Work = -PΔV
To determine the pressure (P) of the gas, we need to use the ideal gas law equation:
PV = nRT
where:
- n is the number of moles
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature (in Kelvin)
Rearranging the equation, we can solve for P:
P = (nRT) / V
Plugging in the values:
- n = 10 mol
- R = 8.314 J/(mol·K)
- T = 273.15 K
- V = V1 = 0.001 m³ (initial volume)
P = (10 mol * 8.314 J/(mol·K) * 273.15 K) / 0.001 m³
Now that we have the pressure (P) and change in volume (ΔV), we can calculate the work done:
Work = -PΔV
Work = -[(10 mol * 8.314 J/(mol·K) * 273.15 K) / 0.001 m³] * 0.019 m³
Simplifying this equation will give us the amount of work done on the gas in joules (J).