Question 8.8: A CONTINUATION OF EXAMPLE 5.4, WITH THE ADDITION SHOWN IN IT...
A CONTINUATION OF EXAMPLE 5.4, WITH THE ADDITION SHOWN IN ITALIC TYPE
A food blender has a cutting-mixing blade driven by a 0.250 \text{hp } electric motor. The machine is initially filled with 1.00 \text{qt } of water at 60.0°\text{F }, 14.7 \text{psia}. It is turned on at full speed for 10.0 \text{min}. Assuming the entire machine is insulated and the mixing takes place at constant pressure, determine the temperature of the water and the amount of entropy produced when the machine is turned off.
First, draw a sketch of the system (Figure 8.8).
The unknowns here are T_2 and _l(S_P)_2. The system is the water in the blender, which we assume to be an incompressible material. The data for the water are as follows:
| \underline{\text{State 1}} | \underrightarrow{\text{Isochoric}} \text{mixing} |
\underline{\text{State 2}} |
| p_1 = 14.7 \text{psia} | \underline{p_2 = p_1 =14.7 \text{psia}} | |
| \underline{T_1 = 60.0°\text{C}} |
The solution to the first part of this problem is given in Example 5.4 as m = 2.08 \text{lbm } and T_2 = 111°\text{F}.
The solution to the second part is determined by the indirect method. Equation (8.1) gives
\begin{matrix}_1(S_P)_2 = m(s_2-s_1)-\underbrace{\int_{Σ}(\frac{\overline{d} Q}{T_b} )}_{0} \\ \quad \quad \quad \quad \quad \quad \quad\quad \quad \quad \quad\text{(insulated system) }\end{matrix}
and, for an incompressible substance,
s_2 −s_1 =c \text{ln} \frac{T_2}{T_1}
so that
_1(S_P)_2 = mc \text{ln} \frac{T_2}{T_1}
or
_1(S_P)_2 = (2.08 \text{lbm})[1.0 \text{Btu/(lbm.R)}]\text{ln} \frac{111 + 459.67}{60.0 + 459.67}
= 0.195 \text{Btu/R}
