A cylinder with a moving piston expands from an initial volume of 0.350L against an external pressure of 2.70atm . The expansion does 251J of work on the surroundings. What is the final volume of the cylinder?

251J x (1 L*atm/101.325 J) = 2.48 L*atm

work = -p(V2-V1)
-(-2.48) = 2.7(V2-0.35)
Solv for V2 in L.

Well, let me calculate that for you. But before I do, did you hear about that mathematician who's afraid of negative numbers? He'll stop at nothing to avoid them!

Now, let's get back to business. To calculate the final volume of the cylinder, we can use the equation:

Work = -P * ΔV

Where Work is the work done on the surroundings (251J), P is the external pressure (2.70atm), and ΔV is the change in volume.

If we rearrange the equation to solve for ΔV, we get:

ΔV = -Work / P

Substituting the values, we have:

ΔV = -251J / 2.70atm

Calculating this gives us:

ΔV = -93.03L

Now, to find the final volume, we add the change in volume to the initial volume:

Final Volume = Initial Volume + ΔV

Final Volume = 0.350L + (-93.03L)

Final Volume = -92.68L

Well, it seems we've encountered a problem here! The result of our calculations yields a negative volume, which is not physically possible. So, it looks like there might be an error in the given information or in our calculations. Time to double-check and make sure we didn't divide by zero or something funny like that!

To find the final volume of the cylinder, we can use the equation for work done in a gas expansion:

Work = Pressure * Change in Volume

We are given the following information:
Initial volume (V₁) = 0.350 L
Pressure (P) = 2.70 atm
Work done (W) = 251 J

We need to find the final volume (V₂).

Using the equation for work, we can rearrange it to solve for the change in volume:

Change in Volume = Work / Pressure

Change in Volume = 251 J / 2.70 atm

Now we can substitute the values and calculate the change in volume:

Change in Volume = 92.963 L

To find the final volume, we need to add the change in volume to the initial volume:

Final Volume (V₂) = Initial Volume (V₁) + Change in Volume

Final Volume (V₂) = 0.350 L + 92.963 L

Final Volume (V₂) = 93.313 L

Therefore, the final volume of the cylinder is 93.313 L.

To find the final volume of the cylinder, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its mechanical energy. In this case, the work done by the expanding cylinder is given as 251J.

Now, work done is defined as:

Work = Force x Distance

In this case, the work done is against an external pressure, which is equal to the force exerted by the piston, multiplied by the distance it moves. Since force is defined as P x A, where P is the pressure and A is the cross-sectional area of the piston, we can rewrite the work equation as:

Work = P x A x Distance

The distance moved by the piston is related to the change in the volume of the cylinder. Since the cylinder is a cylinder with a moving piston, the volume change can be calculated using the formula:

Change in Volume = Area x Distance

Now, we know that the initial volume of the cylinder is 0.350L and the external pressure is 2.70atm. We can convert the volume to meters cubed by multiplying it by 0.001 (since 1L = 0.001m³) and convert the pressure to Pascals by multiplying it by 101,325 (since 1atm = 101,325Pa).

Using these values, we can rearrange the formulas to find the final volume:

Change in Volume = Work / (Pressure x Area)
Final Volume = Initial Volume + Change in Volume

Let's plug in the values and calculate the final volume:

Initial Volume = 0.350L = 0.350 x 0.001 = 0.00035m³
External Pressure = 2.70atm = 2.70 x 101,325Pa = 274,072.5Pa

Now, we need to determine the area of the piston. Without this information, it is not possible to calculate the final volume. Please provide the cross-sectional area of the piston, and we can continue with the calculation.