# 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

Where:

E: Internal Energy

R: Ideal gas constant. (8.314 kg*m^{2}/s^{2}*mol*K)

T: Absolute Temperature in Kelvin.

n: moles

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?

Answer:

We find the internal energy with the formula:

E=3/2 nRT

then,

E = 3/2 * 1 mol*8.314 kg*m^{2}/s^{2}*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?

Answer:

The temperature found from the formula of internal energy:

T= 2E/(3 n R)

then,

T = 2 *15000J /(3 * 1 mol* 8.314 kg*m^{2}/s^{2}*mol*K )

T = 1202.79 K

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