a gas at 10atm pressure occupy a volume of 10L at 300k it is allowed to expand at the constant temperature of 300k under constant external pressure till the volume equilibrate at 100L calculate the work done
543k
first, find the number of moles of gas.
Now, n=PV/RT at the initial condition
change in work= change in PV
change in work= V dP + P dV
but pressure is constant, so dP=0
change in work= P(finalV-initial V) where V is in m^3, P is in Pascals.
Why did the gas go on vacation? Because it needed some "pressure-relief"!
Now let's calculate the work done by our expanding gas. Since the external pressure is constant, we can use the formula:
Work = Pressure x Change in Volume
The pressure is given as 10 atm, so we convert it to Pascals:
10 atm = 10 x 101325 Pa = 1013250 Pa
The change in volume is 100 L - 10 L = 90 L = 90 dm^3
We convert it to cubic meters:
90 dm^3 = 90 x 0.001 m^3 = 0.09 m^3
Now we can calculate the work done:
Work = 1013250 Pa x 0.09 m^3 = 911925 J
So, the work done by our expanding gas is 911925 Joules. That's quite a "gas-tly" performance, don't you think?
To calculate the work done by the gas during expansion, we can use the following formula:
Work = P * ΔV
Where:
P = Constant external pressure
ΔV = Change in volume
In this case, the pressure (P) is given as 10 atm, and the initial volume (Vi) and final volume (Vf) are given as 10 L and 100 L respectively.
So, the change in volume (ΔV) = Vf - Vi = 100 L - 10 L = 90 L.
Substituting the values into the formula, we have:
Work = 10 atm * 90 L
To convert the pressure from atm to SI units (Pascal), we can use the conversion factor 1 atm = 101325 Pa.
Work = 10 atm * 90 L * 101325 Pa/atm
Calculating this, we get:
Work = 91050 J
Therefore, the work done by the gas during expansion is 91050 Joules.
To calculate the work done by the gas during expansion, we need to use the formula:
Work done = -PΔV
Where:
P is the constant external pressure.
ΔV is the change in volume of the gas.
Given:
Initial pressure (P1) = 10 atm
Initial volume (V1) = 10 L
Final volume (V2) = 100 L
Constant external pressure during expansion = P1 = 10 atm
First, we need to calculate the change in volume (ΔV). The change in volume can be calculated by subtracting the initial volume from the final volume:
ΔV = V2 - V1
ΔV = 100 L - 10 L
ΔV = 90 L
Now we can calculate the work done using the formula:
Work done = -PΔV
Work done = -(10 atm)(90 L)
To simplify the calculation, we need to convert atm to joules using the conversion factor: 1 atm = 101.325 joules.
Work done = -(10 atm)(90 L) * (101.325 J/atm)
Work done = -90900 J
Therefore, the work done by the gas during expansion is -90900 Joules. The negative sign indicates that work is done on the gas rather than by the gas.