Internal Energy Formula
The internal energy is the total of all the energies associated with the motion of the molecules in a system. Microscopic forms of energy include those due to the rotation, vibration, translation, and interactions among the molecules of a substance. The more usual formula is given for an ideal gas.
Internal energy = 3/2 (number of moles) * (ideal gas constant) * (Temperature)
The equation is:
E= 3/2 n R T
E: Internal Energy
R: Ideal gas constant. (8.314 kg*m2/s2*mol*K)
T: Absolute Temperature in Kelvin.
Internal Energy Formula Questions:
1) If the temperature of a box full of particles that do not interact between then is 1000 K, having n=1 mol of those particles, what is the internal energy of the system?
We find the internal energy with the formula:
E = 3/2 * 1 mol*8.314 kg*m2/s2*mol*K *1000 K
E = 12471 J
2) The same box before, has an internal energy of 15000 J, what is the value of the temperature?
The temperature found from the formula of internal energy:
T= 2E/(3 n R)
T = 2 *15000J /(3 * 1 mol* 8.314 kg*m2/s2*mol*K )
T = 1202.79 K