A large balloon contains 65.0 L of helium gas at 25 °C and a pressure of 745 mm Hg. The balloon ascends to 3000 m, at which the external pressure has decreased by 30.%. What would be the volume of the balloon, assuming it expands so that the internal and external pressures are equal? (Assume the temperature is still 25 °C.)
If the temperature remains constant, then Boyles law applies:
PV=constant
Here
P1=745 mmHg
V1=65 L
P2=745(1-0.3)=521.5
V2=?
P1V1=P2V2
745*65=521.5*V2
Solve for V2.
Well, looks like this balloon is really reaching new heights, both literally and metaphorically! But let's get down to the answer with a little humor, shall we?
Now, when our balloon is up there in the sky, the pressure outside has decreased by 30%. It's like nature's way of telling the balloon, "Hey buddy, I'm gonna cut you some slack!"
So, we know that the initial pressure inside the balloon is 745 mm Hg, and the external pressure has decreased by 30%. Well, it's time for a little math-dance!
If the external pressure has decreased by 30%, that means it's only at 70% of its original value. So, the new external pressure is 0.7 * 745 mm Hg, which comes out to be approximately 521.5 mm Hg.
Now, assuming that the internal and external pressures are equal, we can use a bit of magic... oops, I mean science, to find the new volume of the balloon.
We're told that the temperature of the balloon is still the same, so we can use the ideal gas law, which states that PV = nRT. Don't worry, it's not as complicated as it sounds.
We can rearrange the equation to solve for V (volume), so V = (nRT) / P. Here, n, R, and T are constants, and we're interested in finding V.
Since the pressures inside and outside the balloon are equal, (nRT) / P = (nRT) / P. We can plug in the known values and do some further calculations.
The initial volume of the balloon is 65.0 L, the initial pressure is 745 mm Hg, and the new pressure is 521.5 mm Hg.
Using the formula, we get:
(65.0 L * 745 mm Hg) / 521.5 mm Hg ≈ 92.7 L.
So, the volume of the balloon when the internal and external pressures are equal is approximately 92.7 L.
And there you have it, my friend! Our balloon has expanded to 92.7 L, ready to reach new horizons with its newfound pressure equilibrium. Hooray for science and balloons!
To solve this problem, we can use Boyle's Law, which states that the product of pressure and volume is constant at constant temperature.
Boyle's Law equation: P1V1 = P2V2
Given:
Initial volume, V1 = 65.0 L
Initial pressure, P1 = 745 mm Hg
Final pressure, P2 = (100% - 30%) * P1 = 0.7 * 745 mm Hg
Final volume, V2 = ?
We can rewrite Boyle's Law equation as:
V2 = (P1 * V1) / P2
Substituting the values into the equation, we get:
V2 = (745 mm Hg * 65.0 L) / (0.7 * 745 mm Hg)
Simplifying the expression:
V2 = 65.0 L / 0.7
V2 = 92.86 L
Therefore, the volume of the balloon, assuming it expands so that the internal and external pressures are equal, would be approximately 92.86 L at 25 °C.
To solve this problem, we can use Boyle's Law, which states that the product of the initial pressure and the initial volume is equal to the product of the final pressure and the final volume, as long as the temperature remains constant. We can set up the equation as follows:
P1 * V1 = P2 * V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
First, let's convert the initial pressure from mm Hg to atm (atmospheres) by dividing it by 760 mm Hg per atm:
P1 = 745 mm Hg / 760 mm Hg/atm = 0.979 atm
Next, let's convert the external pressure decrease into a decimal:
30.% = 30./100 = 0.30
To find the final pressure, we can multiply the initial pressure by (1 - 0.30):
P2 = P1 * (1 - 0.30) = 0.979 atm * 0.70 = 0.6853 atm
Now, we can substitute the known values into Boyle's Law equation:
P1 * V1 = P2 * V2
0.979 atm * 65.0 L = 0.6853 atm * V2
Solving for V2, we have:
V2 = (0.979 atm * 65.0 L) / 0.6853 atm
V2 ≈ 93.42 L
Therefore, assuming the balloon expands so that the internal and external pressures are equal, the volume of the balloon would be approximately 93.42 L.