Yes, assuming that the environment in which the tea is "living" stays a constant temperature. Tea will cool at a constant rate, until it reaches the temperature of the environment (but it will not get any colder than this).
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The rate that tea cools will change with the temperature difference between the tea and the ambient temperature. The larger the difference between the two, the faster the rate will be. As the tea cools closer to room temp, the rate of cooling will decrease.
No. It cools at a rate proportional to the difference between its temperature and that of it's surrounding. The cooler it gets, the closer it will get to room temperature, and the cooling slows down.
There is no difference between them they are same rate constant is another name of specific rate constant
constant rate means that rate which is fixed and can not be changed. varying rate is that rate which is not fixed and can be change easily.
The reaction rate is the rate at which the moles of substance change that varies with both temperature and concentration of the reactants. The specific rate constant is a proportionality constant that will vary only with temperature.