The balloon is filled with helium at a pressure of 120 kPa. The internal energy of the gas is 90 MJ. What is the gas volume?

The internal energy of an ideal gas can be calculated using the formula:
U = (3/2) * (m / M) * R * T.
Ideal gas equation of state (Mendeleev – Clapeyron equation):
p * V = (m / M) * R * T ,.
Therefore, U = (3/2) * p * V, where U is the internal energy of helium (U = 90 MJ = 90 * 10 ^ 6 J), p is the pressure of helium in the balloon (p = 120 kPa = 120 * 10 ^ 3 Pa), V is the volume of helium in the balloon (m ^ 3).
Let’s calculate the volume of helium:
V = 2U / (3p) = 2 * (90 * 10 ^ 6) / (3 * 120 * 10 ^ 3) = 500 m ^ 3.
Answer: The volume of helium in the balloon is 500 m ^ 3.