A hot air balloon is filled with 1.23 × 106 L of an ideal gas on a cool morning (11 °C). The air is heated to 121 °C. What is the volume of the air in the balloon after it is heated? Assume that none of the gas escapes from the balloon.
To solve this problem, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
First, let's convert the given temperatures from Celsius to Kelvin:
Initial temperature (T1) = 11°C + 273.15 = 284.15 K
Final temperature (T2) = 121°C + 273.15 = 394.15 K
Now, let's calculate the initial and final volumes of the gas in the balloon.
Since the problem states that none of the gas escapes from the balloon, we can assume that the number of moles of gas (n) remains constant.
Since the ideal gas law equation PV = nRT can be rearranged as V = (nRT) / P, we can use the ratio of initial and final temperatures and pressures to calculate the final volume:
V2 = (nR * T2) / P2
To solve for V2, we need to know the initial pressure (P1). Unfortunately, the problem does not provide this information. Without the initial pressure, we cannot calculate the final volume accurately.
Therefore, without the initial pressure, we cannot determine the final volume of the air in the balloon after it is heated.