A piston has an external pressure of 7.00 atm. How much work has been done in joules if the cylinder goes from a volume of 0.130 liters to 0.650 liters.
Express your answer with the appropriate units.
work = -p*delta V
work = 7*0.52 = -3.64 L*atm
Multiply by 101.325 if you want the answer in joules.
To calculate the work done by the piston, we can use the formula:
work = -PΔV
Where:
- P is the external pressure (given as 7.00 atm)
- ΔV is the change in volume (0.650 L - 0.130 L)
Substituting the given values into the formula, we get:
work = -7.00 atm * (0.650 L - 0.130 L)
Calculating the difference in volume:
ΔV = 0.650 L - 0.130 L
= 0.520 L
Now we can substitute this value back into the formula:
work = -7.00 atm * 0.520 L
To express the unit in joules, we also need to convert atm to joules. The conversion factor is as follows:
1 atm = 101.325 J
Thus, we can calculate the work done as:
work = -7.00 atm * 0.520 L * 101.325 J/atm
Simplifying the equation gives:
work = -369.31 J
Therefore, the work done by the piston is -369.31 J (we use the negative sign because work done on a gas is negative when the volume increases under external pressure).
To calculate the work done by a piston, we can use the formula:
Work = - Pressure * Change in Volume
Given:
Pressure (P) = 7.00 atm
Initial Volume (V1) = 0.130 liters
Final Volume (V2) = 0.650 liters
First, we need to calculate the change in volume:
Change in Volume (∆V) = Final Volume - Initial Volume
∆V = V2 - V1
∆V = 0.650 liters - 0.130 liters
∆V = 0.520 liters
Now, we can use the formula to calculate the work done:
Work = - Pressure * Change in Volume
Work = - 7.00 atm * 0.520 liters
Since the unit of atm is not in the SI system, we need to convert it to the SI unit of pressure, which is Pascal (Pa).
1 atm = 101325 Pa
So, we can convert the pressure to Pascal:
Pressure = 7.00 atm * 101325 Pa/1 atm
Pressure = 707275 Pa
Now we can calculate the work:
Work = - Pressure * Change in Volume
Work = - 707275 Pa * 0.520 liters
To convert liters to m^3 (cubic meter), we use the conversion factor:
1 liter = 0.001 m^3
So, we can convert the volume to m^3:
Change in Volume = 0.520 liters * (0.001 m^3/1 liter)
Change in Volume = 0.00052 m^3
Now, we can calculate the work:
Work = - 707275 Pa * 0.00052 m^3
According to the equation, work is expressed in Joules (J), so our final answer is:
Work = - 707275 Pa * 0.00052 m^3 = - 367.491 J (rounded to 3 decimal places)
Therefore, the work done by the piston is approximately -367.491 Joules. The negative sign indicates that work is done on the system, as the volume is increasing.