piston whose area is 60 cm2 moves through a distance of 20 cm against a pressure of 3 atm. calculate the work done in joules and calories
First, let's convert the pressure from atm to pascals (Pa):
1 atm = 101325 Pa
3 atm = 3 * 101325 = 303975 Pa
Next, we have to convert the area from cm² to m²:
60 cm² = 0.006 m² (divide by 10000)
Now, let's find the volume that the piston moves through:
Volume (V) = Area (A) * Distance (d)
V = 0.006 m² * 20 cm = 0.006 m² * 0.2 m = 0.0012 m³ (multiply by 0.01 to convert from cm to m)
The work (W) done by the piston can be calculated using the formula:
W = -P * ΔV
Where P is the pressure and ΔV is the change in volume.
W = -303975 Pa * 0.0012 m³ = -364.77 J
The work done is -364.77 Joules. The negative sign indicates that the work is done against the pressure.
To convert the work done in Joules to calories, use the conversion factor:
1 calorie (cal) = 4.184 Joules (J)
W = -364.77 J * (1 cal / 4.184 J) ≈ -87.2 cal
The work done is approximately -87.2 calories.
To calculate the work done by the piston, we can use the formula:
Work = Force × Distance
First, let's calculate the force exerted by the piston. The formula for pressure is:
Pressure = Force / Area
Rearranging the formula to solve for force, we have:
Force = Pressure × Area
Given:
Area = 60 cm²
Pressure = 3 atm
Converting the area to square meters:
1 cm² = 1 × 10^(-4) m²
60 cm² = 60 × 10^(-4) m² = 0.006 m²
Now we can calculate the force:
Force = 3 atm × 0.006 m²
= 0.018 N
Next, we can calculate the work done:
Work = Force × Distance
= 0.018 N × 20 cm
= 0.018 N × 0.20 m (1 cm = 0.01 m)
= 0.0036 J
To convert the work done from joules to calories, we can use the conversion factor:
1 calorie = 4.184 joules.
So,
Work in calories = 0.0036 J × (1 cal / 4.184 J)
= 0.000860 cal
Therefore, the work done by the piston is 0.0036 joules and approximately 0.000860 calories.
To calculate the work done by the piston, we can use the formula:
Work = Force x Distance
First, we need to determine the force exerted by the piston. We can use the formula:
Force = Pressure x Area
Given:
Pressure = 3 atm
Area = 60 cm^2
Convert the pressure from atm to Pascal (Pa), as the SI unit for pressure is measured in Pascal:
1 atm = 101325 Pa
So, the pressure is:
Pressure = 3 atm x 101325 Pa/atm = 303975 Pa
Now, we can calculate the force:
Force = Pressure x Area = 303975 Pa x 60 cm^2
Since the area is in square centimeters (cm^2), we need to convert it to square meters (m^2):
1 cm^2 = 0.0001 m^2
So, the area is:
Area = 60 cm^2 x 0.0001 m^2/cm^2 = 0.006 m^2
Substituting the values into the equation:
Force = 303975 Pa x 0.006 m^2 = 1823.85 N
Now, we can calculate the work done:
Work = Force x Distance = 1823.85 N x 20 cm
Since the distance is in centimeters (cm), we need to convert it to meters (m):
1 cm = 0.01 m
So, the distance is:
Distance = 20 cm x 0.01 m/cm = 0.2 m
Substituting the values into the equation:
Work = 1823.85 N x 0.2 m
Work = 364.77 Joules
To convert Joules to calories, we divide the value by the conversion factor:
1 calorie = 4.184 Joules
So, the work done in calories is:
Work (calories) = 364.77 Joules / 4.184 Joules/calorie
Work (calories) ≈ 87.25 calories
Therefore, the work done by the piston is approximately 364.77 Joules and 87.25 calories.