Determine the final state and temperature of 100 g of water originally at 25.0°c after 50.0 kj of heat have been added to it.

The quantity of heat needed to increase the temperature of a substance by  is given by

where m is the mass of the substance and  is the specific heat of the substance. In our problem, we have  and , which is the speficic heat of the water.
Therefore, we can find the increase in temperature :

The initial temperature of the water was , so the final temperature should be 

So the water should be now vapor.

To be more precise, however, in the transition liquid-vapor part of the heat added to the system is used to break the bonds between molecules, and it does not increase the temperature of the system. The amount of heat needed for the transition between liquid and vapor is given by

where  is the latent heat of vaporization of the water.
However, the initial amount of heat added to the water (50 KJ) is smaller than this number, therefore there isn't enough heat to complete the transition liquid-vapor. Therefore, the water will still be in the liquid-vapor change phase at a temperature of  (which is the temperature at which the phase change starts)

The final state of the water is vapor (gas) and the final temperature is 144.1 ⁰C.

The given parameters;

Mass of the water, m = 100 gInitial temperature of the water, t₁ = 25 °CHeat added to the water, Q = 50 kJ = 50,000 J

The quantity of the heat added to water to cause a change in the state of the water is given as;

Q = mcΔt

where;

c is the specific heat capacity of water = 4,200 J/kg°CΔt is the change in temperature of the water

The change in temperature of the water is calculated as;

The final temperature of the water is calculated as;

Δt = t₂ - t₁

t₂ = Δt  + t₁

t₂ = 119.1 + 25

t₂ = 144.1 ⁰C.

Thus, the final state of the water is vapor (gas) and the final temperature is 144.1 ⁰C.

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