In Section 11.8, suppose the exchanger is made of copper. The exothermic reaction has a rate constant, \(k^{\prime \prime}=0.1\) and a heat of reaction \(\Delta H_{r}=60 \mathrm{~kJ} / \mathrm{mol}\). The hot side fluid has a heat capacity of \(C_{p h}=2000 \mathrm{~J} / \mathrm{kg} \mathrm{K}\), a density \(ho_{h}=850 \mathrm{~kg} / \mathrm{m}^{3}\), a molecular weight of 70, and a mass flow rate of \(0.2 \mathrm{~kg} / \mathrm{s}\). The cold side fluid, \(C p c=4000 \mathrm{~J} / \mathrm{kg} \mathrm{K}\) and a density \(ho_{c}=\) \(1000 \mathrm{~kg} / \mathrm{m}^{3}\). The hot fluid enters the exchanger at a temperature of \(100^{\circ} \mathrm{C}\) and exits at \(55^{\circ} \mathrm{C}\). The cold fluid enters at \(25^{\circ} \mathrm{C}\) and exits at \(45^{\circ} \mathrm{C}\). If the outside surface area of the exchanger, \(A_{s o}=5.03 \mathrm{~m}^{2}\), the corresponding outside overall heat transfer coefficient is \(U_{o}=50\), and the outer diameter of the tube is \(32 \mathrm{~mm}\),

a. What is \(\Delta T_{r}\) ?

b. What is the mass flow rate of the cold fluid needed to meet the restrictions of equation (11.105) where \(H_{0}=z_{0}\) ?

c. What is the amount of heat exchanged in the exchanger?