A rigid tank having a volume of 0.100 m3 contains helium gas at 150 atm. How many balloons can be inflated by opening the valve at the top of the tank? Each filled balloon is a sphere 0.300 m in diameter at an absolute pressure of 1.30 atm.
Well, helium balloons are always a gas at parties! Let's calculate how many balloons we can get from that tank.
First, let's convert the volume of the tank to liters. Since 1 m^3 = 1000 liters, a 0.100 m^3 tank has a volume of 100 liters. That's a decent-sized tank of laughter!
Next, let's find the number of moles of helium gas in the tank using the ideal gas law: PV = nRT. R, the ideal gas constant, is approximately 0.0821 L·atm/(mol·K) (or the number of balloons it takes to make a clown smile).
Rearranging the equation, we have n = PV / RT, where P is the pressure of helium in the tank (150 atm), V is the volume of the tank (100 liters), and T is the temperature in Kelvin. For simplicity, let's assume the temperature remains constant. Just like a clown's smile, it's always at an optimal temperature!
Now, let's convert the diameter of each balloon to its radius: 0.300 m (or 30 cm) becomes 0.150 m (or 15 cm). The radius of laughter!
To find the volume of each balloon (V_balloon), we will use the formula for the volume of a sphere: V_balloon = (4/3) * π * r^3, where r is the radius of the balloon (0.150 m).
Finally, let's calculate the number of balloons we can inflate by dividing the total volume of helium gas in the tank by the volume of each balloon: Number of balloons = n / (V_balloon / 1000), where V_balloon is multiplied by 1000 to convert it from liters to cubic meters.
Now, let's crunch the numbers and find out how many hilarious helium-filled balloons we can get!
To determine the number of balloons that can be inflated, we need to find the volume of each balloon and then calculate how many balloons can fit within the volume of the tank.
First, let's calculate the volume of each balloon. We are given that each balloon is a sphere with a diameter of 0.300 m. The formula for the volume of a sphere is V = (4/3) * π * r^3, where r is the radius of the sphere.
Given the diameter (d) of the balloon is 0.300 m, we can find the radius (r) by dividing the diameter by 2:
r = d/2 = 0.300 m / 2 = 0.150 m
Now, we can calculate the volume of a single balloon:
V_balloon = (4/3) * π * r^3
V_balloon = (4/3) * π * (0.150 m)^3
Next, let's determine the volume of the tank. We are given that the tank has a volume of 0.100 m^3.
Now, we can calculate the number of balloons that can be inflated by dividing the volume of the tank by the volume of a single balloon:
Number of balloons = Volume of tank / Volume of a single balloon
Number of balloons = 0.100 m^3 / V_balloon
To find the number of balloons, we need the value of V_balloon. Let's calculate it:
V_balloon = (4/3) * π * (0.150 m)^3
Now, we can calculate:
Number of balloons = 0.100 m^3 / V_balloon
Calculating the volume of a balloon and then substituting the value back into the equation, we can find the number of balloons that can be inflated.
Divide the number of moles of He in the tank by the number of moles in each balloon.
Use the equation
n = PV/RT for each.
n(tank) = 150*(0.100)/(RT)
n(balloon) = 1.3*(pi/6)(0.3)^3/(RT)
n(tank)/n(balloon) = 15/[1.3*(pi/6)*(0.027)]
Do the numbers