An object with a mass of #2 kg#, temperature of #270 ^oC#, and a specific heat of #18 J/(kg*K)# is dropped into a container with #36 L # of water at #0^oC #. Does the water evaporate? If not, by how much does the water's temperature change?
Rise in the temperature of water
We know that in such interactions heat is gained by one and heat is lost is by the other.
Also that the heat gained/lost is given by
Also from Law of conservation of energy:
In the given problem heat is lost by object and gained by water. Let the final temperatuer of the mixture be
Heat lost by object to cool down from
Heat gained by water to change from
Specific heat of water is
Equating (1) and (2) and solving for the required quantity