# How can energy be added at constant temprature?

In the answer to this question:

Difference between Saturated Liquid and Saturated Steam

How can energy be added with constant temperature? Isn't the energy input itself a change of temperature?

Sorry for the repeat, but I don't have enough reputation to post a comment.

• the energy drives the change of state from solid to liquid or liquid to gas, without causing a change of temperature. Mar 2 '18 at 15:59
• One interesting consequence is that the heat capacity is infinite during a first-order phase transition. Mar 2 '18 at 16:38

Temperature is a measure proportional to the average translational energy (bouncing around) of molecules in a substance, but not energy itself. It is an important measure because energy always transfers from high temperature to low temperature bodies. Heat is the energy change during the transfer.

For Example: When we heat a fluid at a constant pressure.

$Q$ is our heat added $\Delta t$ is our temperature change, $m$ is our mass, $C_p$ is our constant pressure specific heat capacity.

$$Q = mC_p\Delta t$$

Note that a body with a higher $m$ and $C_p$ can be heated by the same amount, but with a lower temperature increase.

Between the saturated liquid and saturated gas points, adding or losing heat does affect the temperature at all, but changes the relative proportions of liquid and gas in the mixture.

• is that law driven from other laws or based on expeirements? Mar 14 '18 at 22:06
• Based on experiments. $Q = mC_p\Delta t$ can be found from adding a known amount of heat to a substance and measuring the temperature change. For steam, we get the relations from various experiments and the results are given in 'steam tables'. Traditionally, temperature has been understood as a macroscopic (large scale) property that we can measure, but we can now derive the idea from what is going on on at microscopic scale, using statistical mechanics and quantum mechanics.
– C.R
Mar 15 '18 at 4:12

At one atmosphere of pressure water boils at a constant 212 F as you add heat.

The heat is used for the state change from liquid to vapor.