# Thermodynamic Work Formula

It is the quantity of energy transferred from one system to another. It is a generalization of the concept of mechanical work in mechanics. It can be related to a variety of physical systems, in the case of an ideal gas is:

Work = (number of moles) * (ideal gas constant) * (change of temperature)

The equation is:

W= n R ΔT

Where:

W: Thermodynamic work

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

ΔT: Absolute Temperature in Kelvin.

n: moles

Thermodynamic work Formula Questions:

1) If the temperature of a box full of particles that do not interact between then is 1000 K and decrease to 500K, having n=1 mol of those particles, what is the work made by the system?

Answer:

We find the work with the formula:

W = n R ΔT

then,

W = 1 mol*8.314 kg*m^{2}/s^{2}*mol*K *500 K

W = 4157 J

2) The same box before, has made a work of 5000 J, what is the value of the temperature if it started at 100 K?

Answer:

The change of temperature is found from the formula of work:

ΔT= W/(n R)

then,

ΔT = 5000 J /( 1 mol* 8.314 kg*m^{2}/s^{2}*mol*K )

ΔT = 601.4 K = T_{f} - T_{i}

T_{f} = 601.4+Ti = 601.4+100K = 701.4 K

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