Time required to raise 1 degree centigrade in 1 liter of water?

Answer 1

To determine the time this will take, you need to know the rate at which heat is being added to the system. The specific heat capacity of a substance is the amount of energy required to raise the temperature of one gram of a substance one degree centigrade. For water at 25oC, the specific heat capacity is 4.184 J*g-1*oC-1. That is, if you have one gram of water, you must add 4.184 Joules of energy (heat) to raise the temperature one one degree centigrade.

The time it takes for the temperature increase to happen depends on how quickly you add the 4.184 J. Adding heat at a rate of 1 Joule/second (which is equivalent to 1 Watt), it is easy to see that it will take 4.814 seconds to raise the temperature of the gram of water one degree centigrade.

The first step to solving your problem, then, is to make your data units compatible with your known constants. We need to convert volume to mass. We do this by means of density. The density of liquid water at standard temperature and pressure is 1g/mL.

1L H2O *1000mL/1L *1g H2O/mL H2O= 1000g H2O

Then, to find the amount of energy required to change the temperature of the mass, we use the specific heat.

1000g H2O *4.184J/(g*K)= 4184 J/oC

Note the units on this last value. They give the amount of energy needed required per degree centigrade of change in the temperature. That is, it requires 4814J to change the temperature of 1000g H2O one degree centigrade. Given the time rate of heat transfer into the system, you can find the time required to make the change. If, for instance, your heat exchange rate is 5 Watts (J/s), you would have

4184 J/oC * 1 second/5 Joules = 836.8 s/oC

This value allows you to calculate the time required for any change in temperature simply by multiplying the number of degrees centigrade temperature change. For one degree, we find

836.8 s/oC *1oC = 836.8s