In physics, the change in entropy is defined as $$dS = \frac{dQ}{T}$$
I tried integrating this. $$\int ds=\frac{1}{T}\int dQ$$ $$S=\frac{Q}{T}+C$$ This essentially converts the change in entropy to absolute entropy. I’m dubious as to whether this is right. At lower temperatures, absolute entropy should be decreasing, not increasing. Yet I did the integration, and this is the result I got. Can anyone explain what I did wrong? And if I didn’t do anything wrong, can anyone explain why this result is so strange?