To develop this problem we will start from the definition of entropy as a function of total heat, temperature. This definition is mathematically described as
[tex]S = \frac{Q}{T}[/tex]
Here,
Q = Total Heat
T = Temperature
The total change of entropy from a cold object to a hot object is given by the relationship,
[tex]\Delta S = \frac{Q}{T_{cold}}-\frac{Q}{T_{hot}}[/tex]
From this relationship we can realize that the change in entropy by the second law of thermodynamics will be positive. Therefore the temperature in the hot body will be higher than that of the cold body, this implies that this term will be smaller than the first, and in other words it would imply that the magnitude of the entropy 'of the hot body' will always be less than the entropy 'cold body'
Change in entropy [tex]\Delta S_{hot}[/tex] is smaller than [tex]\Delta S_{cold}[/tex]
Therefore the correct answer is C. Will always have a smaller magnitude than the change in entropy of the cold object
