Question

A 0.8 m3 balloon contains 130 mol of Helium (an ideal gas). The pressure inside the balloon is 410 kPa. Find the total internal energy of Helium gas inside the balloon.

Answer 1

The total internal energy is equal to the kinetic energy of all the He atoms present in the balloon.
U = KE x n
U = (3/2) k_BT x n
Where (3/2) k_B T is the kinetic energy of one He atom. Multiplying it with the no of atoms present in the ballon gives the total internal energy of gas.
We need to find the temperature of the system,
We can use the Ideal gas equation,
P V = n R T
T = P V / n R
T = 410 x 10³ Pa x 0.8 m³ / 130 x 8.314
T = 303.47 K
The no of He atoms in 0.8 mol is
n = 0.8 mol x 6.022 x 10²³ = 4.818 x 10²³ atoms.
The internal energy
U = (3/2) k_BT x n
U = (3/2) x 1.38 x 10^-23 x  303.47 K x 4.818 x 10²³ atoms
U = 3026.58 J