What is the maximum weight (in grams) that 15 party balloons, each filled with 2 L of helium, can lift at STP? You can assume the weight of the balloon rubber is negligible and the outside air can be treated as pure nitrogen.
To determine the maximum weight that 15 party balloons, each filled with 2 L of helium, can lift at Standard Temperature and Pressure (STP), we need to consider the buoyant force acting on the balloons.
Buoyant force is the upward force exerted on an object submerged in a fluid (in this case, air) and is equal to the weight of the fluid displaced by the object. In this scenario, the buoyant force acting on the balloons is equal to the weight of the air displaced by the balloons.
Let's break down the steps to calculate the maximum weight the balloons can lift:
1. Find the weight of the air displaced by a single balloon:
- Air has a density of approximately 1.225 kg/m³ at STP.
- The volume of a single balloon is 2 L, which is equivalent to 0.002 m³.
- Therefore, the weight of the air displaced by a single balloon is: (1.225 kg/m³) * (0.002 m³) = 0.00245 kg.
2. Calculate the total weight of air displaced by all 15 balloons:
- Since there are 15 balloons, the total weight of air displaced is: 15 * 0.00245 kg = 0.03675 kg.
3. Find the weight equivalent of this amount of air:
- To find the weight equivalent, we need to divide the weight by the density of air.
- The weight equivalent is: (0.03675 kg) / (1.225 kg/m³) = 0.03 m³.
4. Convert the weight equivalent to grams:
- As 1 m³ is equivalent to 1000 L, 0.03 m³ is equivalent to 30 L.
- Therefore, the weight equivalent in grams is: 30 * 1 g/L = 30 grams.
So, the maximum weight that 15 party balloons, each filled with 2 L of helium, can lift at STP is approximately 30 grams.