To determine the change in internal energy of the gas inside the balloon, we need to consider the work done on the gas and the energy transferred to it.
Given:
Work done on the gas = 475 kJ
Energy transferred to the gas = 35 kJ
The change in internal energy (ΔU) can be calculated using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the sum of the heat added to the system and the work done on the system:
ΔU = Q + W
Where:
ΔU = change in internal energy
Q = heat added to the system
W = work done on the system
In this case, the work is done on the gas, so W is positive (+475 kJ). The energy transferred to the gas from the surrounding air is heat, so Q is positive (+35 kJ).
Substituting the given values into the equation:
ΔU = 35 kJ + 475 kJ
ΔU = 510 kJ
Therefore, the gas inside the balloon gained 510 kJ of internal energy.