Final answer:
Using Charles' Law, the new volume of the balloon when the temperature increases from 12°C to 36°C is calculated to be approximately 5.42 liters.
Step-by-step explanation:
To find the new volume of the balloon when the temperature increases, we can use Charles' Law, which states that the volume of a gas is directly proportional to its absolute temperature, assuming that pressure and the number of gas particles remain constant. Charles' Law is represented mathematically as:
V1/T1 = V2/T2, where:
V1 is the initial volume of the gas.
T1 is the initial absolute temperature (in Kelvin).
V2 is the final volume of the gas.
T2 is the final absolute temperature (in Kelvin).
First, we must convert the temperatures from degrees Celsius to Kelvin (K = C + 273.15).
Initial temperature (T1): 12°C = 285.15 K
Final temperature (T2): 36°C = 309.15 K
Starting with the equation V1/T1 = V2/T2 and the provided information:
(5 L / 285.15 K) = (V2 / 309.15 K)
By cross-multiplying and solving for V2, we get:
V2 = 5 L * (309.15 K / 285.15 K) = 5.42 L (approx)
The new volume of the balloon when the temperature increases to 36°C would be approximately 5.42 liters.