A 0.075 -kg ice cube at 0.0^∘ C is dropped into a Styrofoam cup holding 0.33 kg of water at 14^∘

A 0.075 -kg ice cube at 0.0^∘ C is dropped into a Styrofoam...

Key Concepts

Calorimetry

Calorimetry is the measurement of heat transfer during physical changes or chemical reactions. It involves tracking the heat lost or gained by substances as they change temperature or state, and it relies on the principle of energy conservation. In problems involving the mixing of substances at different temperatures or different phases, calorimetry provides the framework to determine the final equilibrium temperature by setting the total heat lost equal to the total heat gained.

Latent Heat of Fusion

The latent heat of fusion is the amount of energy required to change a substance from a solid to a liquid at its melting point, without changing its temperature. This concept is crucial in problems where a substance such as ice is melting, as it factors in the heat needed to overcome the bonds holding the solid structure together, apart from merely raising the temperature of the substance.

Specific Heat Capacity

Specific heat capacity is the measure of the energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a key concept in understanding how different substances respond to heat transfer. In thermal equilibrium problems, it enables the calculation of the energy exchanged by substances as they cool or heat up during the process.

Energy Conservation

Energy conservation in thermal systems states that energy cannot be created or destroyed, only transferred or converted from one form to another. In calorimetry, this principle mandates that the heat lost by warmer objects must equal the heat gained by cooler objects, or the energy consumed in phase changes, allowing for the calculation of final states such as temperature or mass of phase-changed material.

Transcript

00:02 So first we will calculate heat lost by water when it is cooled from 14 degrees celsius to 0 degrees celsius by using the relation q equal to mass time specific heat capacity times change in temperature here mass of water is 0 .33 kilogram into specific heat capacity of water is 4 .1 186 jr per kilogram per degree celsius into changing temperature of water final temperature of water is 0 degree celsius minus initial temperature of water is 14 degrees celsius this gives us heat released by water when it goes equal to minus 1 .93 times 10 to the power 4 june now in the second step we will calculate heat required to melt all the ice at 0 degree celsius by using the relation q ice equal to mass times letting it up fusion here mess of ice is 0 .075 kilogram into letting heat of fusion for ice is 33 .5 times 10 to the power 4 jule pericle gram so this gives us heat required to melt all the ice equal to 2 .5 times 10 to the power 4 jule as magnitude of heat lost by water when it cools is a less and magnitude of heat required to melt all the ice so all the while so all the ice will not be converted into water so some part of ice will be converted into water at 0 degree celsius and other part of ice other part of ice will remain at solid at 0 degree celsius so the overall temperature of the system will be 0 degree celsius now here we want to calculate mass of the melted ice again by using the relation heat released by water plus heat absorbed by melted ice is equal to zero according to law of conservation of energy heat released by water that is equal to mass of water times specific heat capacitor water into change in temperature of water plus heat absorbed by melted ice at zero degrees celsius is equal to mass of melted ice times letting heat of fusion this gives us a let this gives us mass of melted ice equal to minus into mass of water specific heat capacity of water into changing temperature of water upon later heat of fusion now by applying different values here mass of water is 0 .33 kilogram specific heat capacity of water is 4186 jules per kilogram per degree celsius changing temperature of water is here water is cold from 14 degrees celsius to 0 degrees celsius so final temperature is 0 degrees celsius minus initial temperature is 14 degrees celsius upon letting heat of fusion for water is 3 .5 times 10 to the power 4 jule per kilogram this gives us mass of melted ice equal to 0 .0 577 kilogram so this is the mess of melted ice now we can calculate mass of unmelted ice that is equal to total mass of ice of ice of minus mess of melted ice as total mess of ice is 0 .075 kilogram minus mess of melted ice is 0 .05 double 7 kg this gives us mass of unmelted ice equal to 0 .017 kilogram.

07:45 In the second part of this problem if all the ice needs to be melt then magnitude of heat released by water should be equal to heat required to melt all the ice so we can write here released by water plus heat required to melt all the ice is equal to zero so here we want to calculate initial temperature of water so that all the ice melt at 0 degree celsius.

08:59 Heat released by water that is equal to mass of water into specific heat capacitor of water into change in temperature of water...

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