Calculation of Absolute Pressure and Amount of Air
A ball has a volume of 5.27 liters and is at a temperature of 27.0C. A pressure gauge attached to the ball reads 0.25 atmosphere. The atmospheric pressure is 1.00 atmosphere. To calculate the absolute pressure inside the ball and the amount of air it contains, we can use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure in atmospheres
- V is the volume in liters
- n is the number of moles of gas
- R is the ideal gas constant (0.0821 atm·L/mol·K)
- T is the temperature in Kelvin
Given data:
- Volume (V) = 5.27 liters
- Temperature (T) = 27.0C = 300.15K
- Gauge Pressure = 0.25 atm
- Atmospheric Pressure = 1.00 atm
First, let's convert the temperature to Kelvin:
27.0C + 273.15 = 300.15K
Now, we can calculate the absolute pressure inside the ball using the gauge pressure and atmospheric pressure:
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Absolute Pressure = 0.25 atm + 1.00 atm
Absolute Pressure = 1.25 atmospheres
Next, we can calculate the amount of air (moles of gas) inside the ball using the ideal gas law:
PV = nRT
n = PV / RT
n = (1.25 atm * 5.27 L) / (0.0821 atm·L/mol·K * 300.15 K)
n = 0.267 moles of air
Therefore, the absolute pressure inside the ball is 1.25 atmospheres, and the ball contains 0.267 mole of air.
Summary
In summary, the absolute pressure inside the ball is 1.25 atmospheres. The ball contains 0.267 mole of air. The absolute pressure is the sum of the gauge pressure and the atmospheric pressure according to the ideal gas law.
How is the absolute pressure inside a ball calculated given the volume, temperature, gauge pressure, and atmospheric pressure?
The absolute pressure inside a ball can be calculated by adding the gauge pressure to the atmospheric pressure. The ideal gas law equation can be used to determine the amount of air (moles of gas) inside the ball using the volume, temperature, and ideal gas constant.