What is w when a gas is compressed from 49.7 L to 37.7 L using a constant external pressure of 747 Torr?
Note: 760 Torr = 1 atm = 1.01325 bar = 101.325 kPa
work = -p(v2 - v1)
is pressure 747/760?
That answer I gave you will be in units of Liter*atm. You can change that to J by multiplying by 101.325.
101.325 x L*atm = J
Yes. P is 747/760 = ? atm.
so, -(.98)(37.7-49.7)?
I would use another place in the 0.98 since there are three places in the other numbers.
To find the value of w (work done) when a gas is compressed, we can use the formula:
w = -PΔV
where:
- w is the work done by the gas during compression (in Joules, J)
- P is the external pressure applied to the gas (in Pascals, Pa)
- ΔV is the change in volume of the gas (in cubic meters, m³)
First, we need to convert the given volumes from liters to cubic meters. Since 1 L = 0.001 m³, we have:
Initial volume, V₁ = 49.7 L = 49.7 * 0.001 m³ = 0.0497 m³
Final volume, V₂ = 37.7 L = 37.7 * 0.001 m³ = 0.0377 m³
Next, we need to convert the given external pressure from Torr to Pascals. Since 1 Torr = 133.322 Pa, we have:
External pressure, P = 747 Torr = 747 * 133.322 Pa = 99,503.534 Pa
Now we can calculate the change in volume, ΔV:
ΔV = V₂ - V₁ = 0.0377 m³ - 0.0497 m³ = -0.012 m³
Note that the change in volume is negative because the gas is being compressed.
Finally, we can substitute the values into the formula to find w:
w = -PΔV = -(99,503.534 Pa)(-0.012 m³) = 1,194.042 J
Therefore, the value of w when the gas is compressed from 49.7 L to 37.7 L at a constant external pressure of 747 Torr is approximately 1,194.042 Joules.