ChemBench

Entropy Calculator

How much did disorder increase?

Heat transferred, q (J)

Temperature (K)

Entropy change

16.779 J/K

What you entered

Heat transferred, q (J): 5000Temperature (K): 298

1
ΔS = q ÷ T
5000 ÷ 298= 16.7785 J/K

Result

Entropy change: 16.779 J/K

ΔS for this process is 16.779 J/K.

Entropy change from heat transferred at constant temperature

Delta S equals q over T. The same amount of heat produces a larger entropy change when delivered at a lower temperature.

Heat q	Temperature	Entropy change	What this is
500 J	300 K	1.6667 J/K	Small heat input
1,000 J	298.15 K	3.3540 J/K	1 kJ at room temperature
1,000 J	373.15 K	2.6799 J/K	Same heat, hotter system
6,010 J	273.15 K	22.0026 J/K	Melting one mole of ice
40,650 J	373.15 K	108.9374 J/K	Boiling one mole of water

The last row is close to 109 J/mol/K, the value Trouton's rule predicts for the entropy of vaporisation of most liquids. Rows two and three show why the same joule is worth less entropy in a hotter system.

Heat transfer, weighted by temperature

ΔS = q/T reflects that the same amount of heat causes a bigger entropy change at low temperature than at high temperature — disorder increases more dramatically when energy is added to an already-cold, more ordered system.

The arrow of time

Entropy is the quantity behind the second law of thermodynamics — in an isolated system, total entropy only increases, which is part of why time has a direction and why some processes (like an egg unscrambling) never happen spontaneously.

Frequently asked questions

I transfer 500 J of heat to a system at 350 K — what is the entropy change?

ΔS = q/T = 500/350 = 1.43 J/K. The entropy of the system increases by 1.43 J/K.

How does the entropy calculator relate to Gibbs free energy?

Entropy (ΔS) is one of the two inputs to ΔG = ΔH - TΔS. Calculate ΔS here, then plug it into the Gibbs free energy calculator along with ΔH and temperature to determine whether a process is spontaneous.

Can entropy decrease in a system?

Yes — a system's entropy can decrease (like water freezing), but only if the surroundings' entropy increases by at least as much. The total entropy of system + surroundings always increases for any spontaneous process.

Why does the same heat cause a larger ΔS at low temperature?

At low temperature, molecules are already well-ordered, so adding energy creates a proportionally larger disruption. At high temperature, the system is already disordered and the same heat barely changes the distribution.