Here it says to label each process as spontaneous or non-spontaneous. Remember a spontaneous process occurs naturally without the need of outside energy. A non-spontaneous process is an unnatural process that requires a constant flow of energy for it to occur. So all you have to do is imagine if we're describing this process in the real world and you imagine it happening if you can, then it's a natural process and it's spontaneous.
So here it says the sugar cube dissolved in room temperature water. We can picture ourselves taking a sugar cube, placing heated water. We know what would happen. The sugar cube would dissolve in the water. Since it can happen in the natural world, it's spontaneous. Next, mixing of three gases in a container. Gases move randomly when put in a container. So if we took three different gases and put it in a container, we can imagine them mixing together randomly. They don't just stay separate from one another, they just move around freely, so eventually they would mix. So this would be spontaneous as well because no outside energy is needed.
Heat flows from the cold object to warm object. So think about this, what's the natural flow of heat? Heat traditionally moves from a hotter object to a colder object. Here this is saying the exact opposite. So this would be a non-spontaneous reaction because it's an unnatural process. It's not something we would typically see in the natural world. Ice Cube melts at -1°C, well at 0°C. This is the temperature in which water starts to freeze. So if we go even lower than that, then we would expect the water to continue to freeze. So we shouldn't expect it to start melting. The temperature is too low, so here this will be a non-spontaneous process as well.
A ball rolls down a hill. Now here we're going to add a little bit more to this. So we have a ball and let's just say that a gust of wind or something basically pushes it over the cliff. What would be the natural progression of the ball? The ball wouldn't just hover in the air, it would naturally go down the hill because it's naturally going down the hill. It would be a spontaneous process. Here it's aided by gravity, which is not an outside source. It's a natural force.
Finally, we have plant respiration where we have oxygen, glucose, produce, CO2, water and we have some ATP involved. Now we said that when it comes to photosynthesis we need an outside energy source, so it's a non-spontaneous process. The opposite of photosynthesis will be cellular respiration or plant respiration. This is a natural process, so it would be a spontaneous process and that's how we describe each one of these processes as being either spontaneous or non-spontaneous.