How would you define a spontaneous and a non spontaneous process?
See explanation and watch the video.
A spontaneous process is one that happens without the intervention of the outside.
A non spontaneous process would not happen without the intervention of the outside.
For more details and scientific explanation, I recommend this video that explains in details spontaneity.
Thermodynamics | Spontaneous Process & Entropy.
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A spontaneous process occurs without outside influences such as the incorporation of energy into the system, the usage of a catalyst, or the addition of extra reagent to push the equilibrium forward.
An example is when a concentration gradient promotes glucose through a channel protein for glycolysis. It does not require input of energy to instigate it.
A nonspontaneous process requires such outside influences to occur.
An example is hydrolysis of a peptide bond. You need an enzyme such as trypsin to make it happen. Otherwise, it's way too slow to happen in our lifetimes. That's great, because otherwise we would turn to mush pretty often.
Mathematically:
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A spontaneous process is one that occurs naturally without requiring external input or intervention, driven by favorable changes in entropy and enthalpy. In contrast, a non-spontaneous process requires external energy input to occur, typically going against the natural direction of change in entropy and enthalpy.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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