(Solved): solve complete  A well stirred batch reactor equipped with an electric heating mantle is charg ...

solve complete 

A well stirred batch reactor equipped with an electric heating mantle is charged with a liquid reaction mixture. The reactants must be heated from an initial temperature \( T_{l} \) to a final temperature \( T_{2} \) before the reaction can take place. Make sure you convert all units to metric. 1. Write down the unsteady energy balance or the unsteady first law 2. Solve the simple differential equation for the temperature as a function of time 3. Solve/derive an equation for the time at which the temperature reaches \( 257^{\circ} \mathrm{C} \) 4. Use a weighted average to determine the average specific heat \( C v \). Use the weighting factors as the ratio of the mass of the reactant to the total mass and the ratio of the mass of the reactor to the total mass \[ \bar{C}_{v}=\frac{M_{\text {Reactants }}}{M_{\text {Reactants }}+M_{\text {Reactor }}} C_{v \mid \text { Reactants }}+\frac{M_{\text {Reactor }}}{M_{\text {Reactants }}+M_{\text {Reactor }}} C_{v \mid \text { Reactor }} \]