Work out entropy change instantly with clear inputs, formula shown and shareable results.
Because temperature changes during heating, entropy must be integrated: dS = mc ln(T2/T1). Warming 1 kg of water from 300 K to 350 K transfers 209 kJ and raises entropy by 644 J/K. The ratio of heat to entropy gives an effective mean temperature of 324.4 K, slightly below the arithmetic mean.
Entropy change on heating
dS = m c ln(T2 / T1)
Heat transferred
Q = m c (T2 - T1)
That only works at constant temperature. When temperature varies, each small amount of heat is divided by the temperature at that moment, giving the logarithm.
For one object, yes - cooling it lowers its entropy. The second law requires only that the total including the surroundings does not fall.