**Title: Calculating Energy Required for Phase Changes and Temperature Increases****Introduction:**To understand how much energy is needed to convert ice to water and increase its temperature, let's explore the calculation involved in this transformation.**Problem Statement:**Calculate the energy required (in Joules) to convert 9.6 kg of ice at -31°C to water at 84°C.**Given Values:**- **Specific heat of water, \( c_{\text{water}} = 4186 \, \text{J/kg°C} \)**- **Latent heat of fusion of ice, \( L_F = 3.33 \times 10^5 \, \text{J/kg} \)**- **Specific heat of ice, \( c_{\text{ice}} = 2090 \, \text{J/kg°C} \)****Discussion:**When converting ice at a sub-zero temperature to water above room temperature, the process involves several stages:1. **Heating the ice from -31°C to 0°C.**2. **Melting the ice at 0°C to form water.**3. **Heating the resultant water from 0°C to 84°C.**By calculating the energy for each stage and summing them up, we determine the total energy required. Each stage utilizes specific heat capacities and latent heat properties to facilitate these transformations. **Formulas:****Specific Heat:**- \( c \equiv \frac{Q}{m \Delta T} \) (J/kg · °C)- \( Q = mc(T_f - T_i) \)**Mixtures:**- \( Q_{\text{cold}} = -Q_{\text{hot}} \)**Latent Heat:**- Phase change: \( Q = \pm mL \)**Thermal Conductivity:**- \( Q/t = \text{Power} = P = kA \frac{(T_h - T_c)}{L} \)**Stefan’s Law of Radiation:**- \( P = \sigma A e T^4 \)---**Explanation:**- **Specific Heat:** This set of equations is used to calculate the amount of heat (\(Q\)) required to change the temperature of a mass (\(m\)) by a certain temperature difference (\(\Delta T\)). The specific heat (\(c\)) is expressed in joules per kilogram per degree Celsius. - **Mixtures:** This equation indicates that in a thermal mixture, the heat lost by the hot substance (\(Q_{\text{hot}}\)) equals the heat gained by the cold substance (\(Q_{\text{cold}}\)).- **Latent Heat:** This formula is for phase changes, where \(L\) is the latent heat. The heat transferred (\(Q\)) during a phase change depends on the mass (\(m\)) and the latent heat of the substance.- **Thermal Conductivity:** This equation calculates the power (\(P\)) or heat transfer rate, taking into account the conductivity (\(k\)), the area (\(A\)), and the temperature difference between the hot (\(T_h\)) and cold sides (\(T_c\)) over a distance (\(L\)).- **Stefan’s Law of Radiation:** This formula describes the power (\(P\)) radiated by a body with area (\(A\)), emissivity (\(e\)), and temperature (\(T\)), using the Stefan-Boltzmann constant (\(\sigma\)).

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Answered: How much energy is needed (in Joules)…

How much energy is needed (in Joules) to convert 9.6 kg of ice at -31° C to water at 84°C? Specific heat of water, cwater = 4186 J/kg-C°,

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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