How much work is done by 3 moles of gas when they triple their volume at a constant temperature of 400 K ?
show work please
To find out the amount of work done by a gas, we can use the equation:
Work = -P(V2 - V1)
where P is the pressure of the gas and V1 and V2 are the initial and final volumes, respectively.
Since the problem states that the gas tripled its volume, we can assume that the initial volume, V1, is the volume before tripling, and the final volume, V2, is three times the initial volume.
To solve the problem, we need to know the pressure of the gas. Unfortunately, the problem does not provide this information. However, we can assume that the pressure remains constant throughout the process, as the temperature is constant.
Therefore, we can rewrite the equation using the ideal gas law:
Work = -nRT * ln(V2/V1)
Where n is the number of moles of gas, R is the ideal gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and ln is the natural logarithm.
Now, we can calculate the work done:
n = 3 moles (given)
R = 8.314 J/(mol·K) (constant)
T = 400 K (given)
V1 = initial volume
V2 = 3 * V1 (final volume)
Substituting the values into the formula:
Work = -3 * 8.314 J/(mol·K) * 400 K * ln(3)
Calculating this expression, we get:
Work ≈ - 3 * 8.314 J/(mol·K) * 400 K * 1.0986
Work ≈ - 11,116 J (rounded to the nearest whole number)
Therefore, 3 moles of gas do approximately -11,116 J (or 11,116 J of work in opposite to the direction of expansion) when tripling their volume at a constant temperature of 400 K.