Question

You have a balloon covering the mouth of a flask filled with air at 1 atm. You apply heat to the bottom of the flask until the volume of the balloon is equal to that of the flask. a. Which has more air in it, the balloon or the flask? Or do both have the same amount? Explain. b. In which is the pressure greater, the balloon or the flask? Or is the pressure the same? Explain.

Short answer

a. Both the balloon and the flask have the same amount of air, as they have the same volume and the air had the same initial conditions of pressure and temperature. b. The pressure inside the flask is greater than that inside the balloon after applying heat to the flask, because the air inside the flask is fighting against the atmosphere to inflate the balloon and faces less resistance once it enters the balloon.

Step-by-step solution

Understanding the Initial Condition

Before applying heat, the mouth of the flask is covered by the balloon, and the air is enclosed inside the flask at 1 atmospheric pressure (1 atm). The air inside the balloon and the flask is at the same initial conditions (same pressure, temperature, and volume).

Applying Heat to the Flask

When we apply heat to the flask, the temperature of the air inside the flask increases. According to the ideal gas law, \(PV = nRT\), where P is the pressure, V is the volume, n is the amount of gas (in moles), R is the ideal gas constant, and T is the temperature (in Kelvin). As the temperature increases, the volume of the air in the flask will also increase. Since the balloon is covering the mouth of the flask, the air will expand into the balloon until the balloon's volume is equal to that of the flask. a.

Comparing the Amount of Air

Since the balloon and flask have the same volume at the end of the experiment, and because the air inside them has the same initial conditions of pressure and temperature, the amount of gas in both the balloon and the flask at the end of the experiment will be the same. According to the ideal gas law, the product nT should be equal if the product PV is equal. Therefore, the balloon and the flask have the same amount of air. b.

Comparing the Pressure

The pressure inside the flask and the balloon is equal initially as they are both subject to atmospheric pressure. However, upon heating the flask, the temperature of the air inside increases, causing an increase in volume into the balloon. Since the balloon expands, it means that there is a higher pressure inside the flask than there is inside the balloon. This is because the air inside the flask is fighting against the atmosphere to inflate the balloon, whereas once the air has entered the balloon, it faces less resistance. In conclusion, the pressure inside the flask is greater than that inside the balloon after applying heat to the flask.