The Change of Temperature with the Addition of Heat

Question: What is the temperature of solid water (ice)?

a

$\approx 0^\circ$ C

b

$\approx 273$K

c

Any of the above (a and/or b)

d

$\approx 10^\circ$ C

e

$\approx -10^\circ$

f

any of the above (d and/or e and/or c)

Consider a mole of ice at $-100^\circ$C that has heat added to it at a constant rate ( $\dot{q} =$ constant) and a constant pressure. (Slow enough so that the body has a uniform temperature; i.e., reversibly at constant atmospheric pressure). What will be the temperature as a function of time?

Figure 14-1: Heating up cold ice at a constant rate.

What is the slope of the initial part of the curve (Region I)?

$$\input{equations/92A}$$ (14-1)

Therefore the slope is $\frac{1}{C_P}$:

Region I

Slope = $\frac{1}{C_{P(\mbox{(solid)}}}$

Region III

Slope = $\frac{1}{C_{P(\mbox{(liquid)}}}$

Question: What is happening in Region II?

Question: What is the heat absorbed in Region II? Where does it go?

$$\input{equations/92B}$$ (14-2)

This is equivalent to the heat absorbed by the system at constant temperature--we identified this quantity with the state function enthalpy, $H= U + PV$. The change in the constant pressure heat state function $\Delta H$, is the heat absorbed during the transformation.