1. Descriptive of how an individual cannot be satisfied or has an insatiable greed for an activity or pursuit: Tom was unappeasably thirsty and so drank about 2 litres of water in a very short time!
2. Pertaining to how a person cannot be calmed; how a state of peace, calm, or contentment cannot be achieved: Mary was unappeasably distressed after losing her job and having so many debts to pay.