A hot-air balloon has a volume of 970 L at 28 degrees C . To what temperature must it be heated to raise its volume to 1200 L , assuming the pressure remains constant?
(V1/T1) = (V2/T2)
so it would be 970L/28degreesC=1200L/x? I did that and I got 34.6 and when i put it into my answer slot on MasteringChemistry it says its wrong.
Am I doing something wrong?
Yes. C must be in kelvin.
To find the temperature to which the hot-air balloon must be heated, we can use the combined gas law, which states that the ratio of the initial pressure to the initial temperature is equal to the ratio of the final pressure to the final temperature, assuming constant pressure.
Let's denote the initial volume, temperature, and final volume, temperature as V1, T1, V2, and T2, respectively.
Given:
Initial volume (V1) = 970 L
Initial temperature (T1) = 28°C + 273.15 (convert to Kelvin) = 301.15 K
Final volume (V2) = 1200 L
We need to find the final temperature (T2).
Using the combined gas law, we have:
(P1 * V1) / T1 = (P2 * V2) / T2
Since the question states that the pressure remains constant, we can cancel out the pressure terms:
(V1 / T1) = (V2 / T2)
Now, plug in the given values:
(970 L / 301.15 K) = (1200 L / T2)
Cross-multiply:
(970 L * T2) = (1200 L * 301.15 K)
Divide both sides by 970 L:
T2 = (1200 L * 301.15 K) / 970 L
Evaluate the expression:
T2 ≈ 373.45 K
The hot-air balloon must be heated to approximately 373.45 K (or 100.3°C) in order to raise its volume to 1200 L, assuming the pressure remains constant.