Question

a chemical engineer needs to calculate the amount of coolant required to cool a reaction vessel to a specific temperature. the coolant reduces the temperature of the vessel by absorbing heat from it. during this process, the coolant evaporates. which equation should the engineer use to determine how much coolant is required?
options (boxes with symbols like δh, -δh etc.) are shown but text of options is partially visible as: δh..., -δh..., -δh..., δh...

Explanation:

Step1: Identify the Process

The problem involves a coolant absorbing heat from a reactor, so we're dealing with heat transfer and enthalpy change. The coolant's enthalpy change relates to the heat it absorbs.

Step2: Recall Thermodynamic Formulas

For a process where a substance (coolant) absorbs heat, the heat absorbed \( q \) is related to the enthalpy change of the coolant. If the reactor is releasing heat (exothermic for the reactor), the coolant is absorbing heat (endothermic for the coolant), so \( q_{\text{coolant}} = -\Delta H_{\text{reactor}} \) (since heat lost by reactor is heat gained by coolant). But also, the enthalpy change of the coolant \( \Delta H_{\text{coolant}} \) should equal the heat it absorbs (at constant pressure, which is typical in such processes), so \( \Delta H_{\text{coolant}} = q_{\text{coolant}} = -\Delta H_{\text{reactor}} \). Wait, but looking at the options, one of them is \( -\Delta H_{\text{reactor}} \) (or similar). Wait, maybe the key is that the coolant's enthalpy change is equal to the negative of the reactor's enthalpy change (because reactor loses heat, coolant gains it). So the correct equation should relate the coolant's enthalpy change to the negative of the reactor's. Alternatively, if we consider the heat absorbed by coolant \( q = \Delta H_{\text{coolant}} \), and the reactor's \( \Delta H_{\text{reactor}} = -q \), so \( q = -\Delta H_{\text{reactor}} \), hence \( \Delta H_{\text{coolant}} = -\Delta H_{\text{reactor}} \). But looking at the options, maybe the correct one is \( -\Delta H_{\text{reactor}} \) (the third option, maybe? Wait, the options are: \( \Delta H_{\text{coolant}} \), \( -\Delta H_{\text{coolant}} \)? No, the user's image shows options like \( \Delta H_{\text{coolant}} \), \( -\frac{\Delta H}{\text{coolant}} \)? Wait, maybe OCR issues. Wait, the problem is about a chemical engineer calculating coolant needed, so the relevant equation is that the heat absorbed by coolant is equal to the negative of the reactor's enthalpy change (since reactor releases heat, \( \Delta H_{\text{reactor}} \) is negative if we take heat absorbed as positive). Wait, maybe the correct formula is \( -\Delta H_{\text{reactor}} \), because the coolant's enthalpy change is the heat it gains, which is equal to the heat the reactor loses, so \( \Delta H_{\text{coolant}} = - \Delta H_{\text{reactor}} \) (since \( \Delta H_{\text{reactor}} = q_{\text{reactor}} \), and \( q_{\text{coolant}} = -q_{\text{reactor}} \), so \( \Delta H_{\text{coolant}} = - \Delta H_{\text{reactor}} \)). So the engineer should use \( -\Delta H_{\text{reactor}} \) (or the option that represents the coolant's enthalpy change as negative of reactor's). Wait, maybe the correct option is the one with \( -\Delta H_{\text{reactor}} \), assuming the options include that. But based on thermodynamics, the heat absorbed by coolant is \( q = \Delta H_{\text{coolant}} \), and \( q = - \Delta H_{\text{reactor}} \) (because reactor's \( \Delta H \) is \( q_{\text{reactor}} \), and \( q_{\text{coolant}} = - q_{\text{reactor}} \)). So the engineer should use \( \Delta H_{\text{coolant}} = - \Delta H_{\text{reactor}} \), so the formula is \( -\Delta H_{\text{reactor}} \) (or the option that is the negative of the reactor's enthalpy change).

Answer:

The correct formula is \( -\Delta H_{\text{reactor}} \) (assuming the third option in the image is \( -\Delta H_{\text{reactor}} \); if options are labeled, e.g., C. \( -\Delta H_{\text{reactor}} \), then the answer is C. \( -\Delta H_{\text{reactor}} \)).