A balloon filled with helium has a volume of 30.0 L at a pressure of 100 kPa and a temperature of 15.0 Celsius. What will the volume of the balloon be if the temperature increased to 80.0 Celsius and the pressure remains constant?
(V1/T1) (V2/T2)
T must be in kelvin.
To find the new volume of the balloon, we can use the combined gas law formula:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 and P2 are the pressures,
V1 and V2 are the volumes, and
T1 and T2 are the temperatures.
In this case, we are given:
P1 = 100 kPa
V1 = 30.0 L
T1 = 15.0 Celsius = 273 + 15 = 288 K
T2 = 80.0 Celsius = 273 + 80 = 353 K
Since the pressure remains constant (P1 = P2), we can simplify the equation to:
(V1) / (T1) = (V2) / (T2)
Now we can plug in the known values:
(30.0 L) / (288 K) = (V2) / (353 K)
To solve for V2, we can cross-multiply:
V2 = (30.0 L) * (353 K) / (288 K)
V2 ≈ 36.77 L
Therefore, the volume of the balloon will be approximately 36.77 L when the temperature increases to 80.0 Celsius, assuming the pressure remains constant.