Consider the following plot (temperature against time) for two substances A and B of equal masses being heated uniformly at $6 \; \text{cal} \, \text{s}^{-1}$. We are required to find the ratio of heats absorbed during the fusion of the substances.
This inadequate solution was given, where they relate the heats using time.
I don't understand it fundamentally. Why/How is time even related to heat? Is what was given a known result that I'm unaware of?
Any help is appreciated!
You're told that both substances are being given heat (energy) at a rate of $6 \text{ cal s}^{-1}$. This means that every second, your substance gains $6 \text{ cal}$ of energy. All you have to do is work out how many seconds each substance is in their "fusion" phases and multiply rate by time. The "known result" you're looking for is just $$\text{total amount of stuff}=\text{rate that stuff is given}\times\text{time it is happening for}$$ Check units: $$\text{cal}=\text{cal s}^{-1}\times\text{s}$$
Why/How is time even related to heat?
"Heat" is just energy, so the more time we spend pumping this energy into a substance, clearly the more energy that substance is going to absorb overall.
