Calculation of Absolute Pressure and Amount of Air Inside a Ball

Introduction

A ball has a volume of 5.27 liters and is at a temperature of 27.0°C. A pressure gauge attached to the ball reads 0.25 atmosphere. The atmospheric pressure is 1.00 atmosphere.

Calculation

To calculate the absolute pressure inside the ball and the amount of air it contains, we need to consider the given values:
  • Volume (V) = 5.27 liters
  • Temperature (T) = 27.0°C
  • Gauge Pressure (Pg) = 0.25 atmosphere
  • Atmospheric Pressure (Patm) = 1.00 atmosphere

Absolute Pressure Calculation

The absolute pressure inside the ball can be calculated using the formula:

Pabs = Pg + Patm

Substituting the given values:

Pabs = 0.25 + 1.00 = 1.25 atmospheres

Therefore, the absolute pressure inside the ball is 1.25 atmospheres.

Amount of Air Calculation

The amount of air in moles inside the ball can be calculated using the ideal gas law:

n = PV / RT

Substituting the values and constants:

n = (1.25 atm * 5.27 L) / (0.0821 L*atm/mol*K * 300 K) ≈ 0.267 moles of air

Therefore, the ball contains approximately 0.267 mole of air.

What is the absolute pressure inside the ball and the amount of air it contains?

The absolute pressure inside the ball is 1.25 atmospheres and the ball contains 0.267 mole of air.

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