Suppose that, on a day when the outside temperature is 15 degrees Celsius, we fill a balloon with pure nitrogen gas, of which the molar mass is 28 grams per mole. Now suppose that we want to heat up a second (equally large) balloon containing air, such that it generates the same amount of lift.
To what temperature (in degrees Celsius) should we heat up the second balloon?
Polat A. You are a brave man but also fool . Aslan A. has told you lie thought we've believed him.
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David my brother ın my opinion he used air's molar constant but he didn't show you
only the dead men see
pls how did you arrive at this 24.95
Çakır 39 count
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L=ρVg(1−2828.97)=ρVg⋅0.0334829 is the lift of nitrogen to air
now T/(T+ΔT) for hot air balloon, the T is 288K and we know 15 celsius was outside temperature. so ΔT is 9.9 and add 15 gives about 25 C.
24.95
To find the temperature to which we need to heat up the second balloon, we need to consider the concept of ideal gas law and the relationship between temperature and pressure for a gas.
The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
We know that both balloons are equally large, so we can assume they have the same volume. The second balloon contains air, which is a mixture of gases where nitrogen makes up about 78%. To simplify the calculation, let's assume the air in the second balloon behaves similarly to pure nitrogen.
For the first balloon filled with pure nitrogen, since we know the molar mass is 28 grams per mole, we can calculate the number of moles of nitrogen using the given mass. Let's say the mass of nitrogen in the first balloon is m grams. Then, the number of moles (n₁) is given by n₁ = m / 28.
Since both balloons have the same volume and pressure, according to the ideal gas law, the number of moles (n₂) of gas in the second balloon should be equal to n₁. Therefore, we have n₂ = m / 28.
Now, we can find the temperature to which we need to heat up the second balloon using the ideal gas law. Since the volume, number of moles, and gas constant are constant for both balloons, we can simplify the equation as follows: P₁ × T₁ = P₂ × T₂.
The pressure in both balloons should be the same, so P₁ = P₂. Let's substitute n₁ and n₂ into the equation: (m / 28) × T₁ = (m / 28) × T₂.
Canceling out the terms with n in the equation, we have T₁ = T₂. So, the temperature we need to heat up the second balloon to generate the same lift as the first balloon filled with pure nitrogen is the same as the temperature on the day, which is 15 degrees Celsius.
Therefore, to generate the same amount of lift, we need to heat up the second balloon to 15 degrees Celsius.