Hot air balloons gain their lift from the reduction in the density of air that occurs when the air in the envelope is heated. To what temperature should you heat a sample of air (initially at 374 K) to increase its volume by 13%? Answer in units of K.
thanks for helping !
1- C
2-B
3-C
4-B,C
5- D
6- D
7- C
8- B
9- C
10-C
Hannah is 100% correct! ^_^ Thanks!
Hannah is correct! :P
(V1/T1) = (V2/T2)
Since they don't give a volume, just make up a convenient number for V1(say 100 L) then V2 will be 113 L.
To solve this problem, we can use the ideal gas law, which states:
PV = nRT
Here, P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Given that we want to increase the volume by 13%, we can calculate the final volume by multiplying the initial volume by 1.13.
Let's assume the initial pressure, number of moles, and the ideal gas constant remain constant in this scenario.
Therefore, we can rewrite the equation as:
P(V * 1.13) = nR(Tf)
Dividing both sides by P, we get:
V * 1.13 = (nR/P) * Tf
Since (nR/P) is a constant value, we can simplify the equation to:
V * 1.13 = K * Tf
Now, we can substitute the initial temperature, Tf, and the volume into the equation to solve for Tf:
374 K * 1.13 = K * Tf
Simplifying further:
Tf = (374 K * 1.13) / K
Tf = 422.62 K
Therefore, to increase the volume by 13%, you would need to heat the sample of air to approximately 422.62 Kelvin.