A sample of gas in a balloon has an initial temperature of 28 and a volume of 1360 . If the temperature changes to 86, and there is no change of pressure or amount of gas, what is the new volume, , of the gas?
Express the volume numerically in liters.
28 WHAT? 1360 WHAT?
Use (V1/T1) = (V2/T2)
Don't forget T1 and T2 must be in kelvin.
To solve this problem, we can use the combined gas law formula, which states:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 and P2 are the initial and final pressures of the gas.
V1 and V2 are the initial and final volumes of the gas.
T1 and T2 are the initial and final temperatures of the gas.
In this case, the pressure and amount of gas are constant, so we only need to consider the temperature and volume.
Given:
- Initial temperature (T1) = 28 °C
- Initial volume (V1) = 1360 liters
- Final temperature (T2) = 86 °C
First, let's convert the temperatures from Celsius to Kelvin, as the gas law requires temperatures to be in Kelvin:
T1 (Kelvin) = 28 + 273 = 301 K
T2 (Kelvin) = 86 + 273 = 359 K
Now we can plug the values into the formula:
(P1 * V1) / T1 = (P2 * V2) / T2
Since the pressure and amount of gas are constant, we can eliminate them from the equation. Therefore, the equation simplifies to:
V1 / T1 = V2 / T2
Substituting the known values, we have:
1360 / 301 = V2 / 359
Now we can solve for V2:
V2 = (1360 / 301) * 359
Calculating this, we find:
V2 ≈ 1618.94 liters
Therefore, the new volume of the gas, V2, is approximately 1618.94 liters.