A gas-forming reaction produces 1.35 m3 of gas against a constant pressure of 143.0 kPa. Calculate the work done by the gas in joules.
Why did the gas go to school? To work on its "gas"timation skills! Now, let's calculate the work done.
The work done by a gas can be determined using the formula:
Work = Pressure * Change in Volume
So, in this case, we have:
Pressure = 143.0 kPa
Change in Volume = 1.35 m3
Let's convert the pressure into Pascals because the SI units are much cooler:
1 kPa = 1000 Pa
Pressure = 143.0 kPa = 143.0 * 1000 Pa = 143000 Pa
Now we can calculate the work done:
Work = Pressure * Change in Volume
Work = 143000 Pa * 1.35 m^3
Calculating this, we find:
Work = 193050 Joules
Voila! The work done by the gas is 193050 Joules, which is no laughing matter!
To calculate the work done by the gas, we can use the formula:
Work = Pressure * Volume
Given:
Pressure = 143.0 kPa
Volume = 1.35 m^3
First, we need to convert the pressure from kilopascals to pascals:
1 kPa = 1000 Pa
Thus, the pressure in pascals is:
143.0 kPa * 1000 Pa/kPa = 143000 Pa
Now we can calculate the work:
Work = Pressure * Volume
= 143000 Pa * 1.35 m^3
Finally, we can calculate the work done by the gas:
Work = 192,750 J (rounded to three significant figures)
Therefore, the work done by the gas is approximately 192,750 Joules.
To calculate the work done by the gas, we need to use the formula:
Work (W) = Force (F) x Distance (d) x cosθ
In this case, the force is the pressure exerted by the gas, and the distance is the change in volume.
First, we need to convert the initial volume of gas, which is given as 1.35 m^3, into an SI unit such as liters.
1 m^3 = 1000 L
Therefore, the initial volume of gas is 1.35 m^3 * 1000 L/m^3 = 1350 L.
Next, we need to calculate the change in volume, which is the final volume minus the initial volume:
Change in Volume (ΔV) = Final Volume - Initial Volume
Since the gas has produced 1.35 m^3 of gas, the final volume is the initial volume plus the gas produced:
Final Volume = Initial Volume + Gas Produced = 1350 L + 1.35 m^3 * 1000 L/m^3 = 1350 L + 1350 L = 2700 L
Therefore, the change in volume is:
ΔV = 2700 L - 1350 L = 1350 L
Now, we have the pressure (143.0 kPa) and the change in volume (1350 L). However, the equation Work = Pressure x Change in Volume assumes that the angle (θ) between the force and the distance is 0°, meaning the force and distance are in the same direction. In this case, since pressure is constant and the volume is increasing, the angle is 0°, and cosθ is equal to 1.
Therefore, we can calculate the work:
Work = Pressure x Change in Volume x cosθ = 143.0 kPa * 1350 L * cos(0°)
Lastly, we need to convert kPa to Pa, as the SI unit for pressure is Pascal (Pa):
1 kPa = 1000 Pa
Therefore, the work can be calculated as:
Work = 143.0 kPa * 1350 L * cos(0°) * 1000 Pa/kPa
Now we can plug in the values and calculate the work done by the gas.
Work = 143.0 kPa * 1350 L * 1000 Pa/kPa = 193,050,000 J
Therefore, the work done by the gas is 193,050,000 Joules (J).
w=-P(delta)V
w=(-143.0kPa)(1.35m^3)
w=193.05kJ
193.05*1000=193050J