If 10.0 g of ice at -10.0^∘ C and 20.0 g of liquid water at 100 . ^∘ C are mixed in an insulat

If 10.0 g of ice at -10.0^∘ C and 20.0 g of liquid water...

Key Concepts

Conservation of Energy

This principle states that energy cannot be created or destroyed, only transferred or transformed. In a closed system, such as an insulated container, the heat lost by a warmer substance must equal the heat gained by a cooler substance. This concept is crucial when analyzing how different parts of a system interact thermally to reach equilibrium.

Calorimetry

Calorimetry is the science of measuring the amount of heat exchanged in a chemical or physical process. It involves tracking how energy is transferred during processes like heating, cooling, or phase changes, which is essential for understanding and predicting the final temperatures in mixed systems.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. This property helps in determining how much energy a substance can absorb or release for a given change in temperature, which is critical for calculating temperature changes in thermal exchange problems.

Latent Heat of Fusion

Latent heat of fusion is the amount of heat required to convert a unit mass of a substance from a solid to a liquid at its melting point without a change in temperature. This concept is important when dealing with phase changes, as energy is absorbed or released during the melting or freezing process without altering the temperature until the phase change is complete.

Thermal Equilibrium

Thermal equilibrium occurs when two bodies in contact no longer exchange heat, and they eventually reach the same temperature. Understanding this concept is essential when analyzing the end state of a system where different substances, initially at different temperatures, mix and gradually reach a uniform temperature.

Transcript

00:01 In this problem, we have a mixture of ice and liquid water 100 degrees celsius.

00:09 And it's in an insulated container, so there's no heat loss to the surroundings.

00:14 We want to know what is the final temperature of this mixture.

00:18 So we have a few things happening here.

00:20 First, the ice needs to be heated up to 0 degrees celsius, which is its melting point.

00:26 So we're going to assume that the ice is definitely going to melt.

00:30 Because as you can see, the water is already at 100 degrees celsius, so the ice is definitely melting from this hot water.

00:41 So set up qaqa's mc delta t, plug in the mass of the ice, 10 grams, and then use the specific heat of ice.

00:54 So make sure you're using specific heat of ice, not of water.

00:58 And be sure that this is in the correct units, so i'm using...

01:05 Jules over gram times degrees celsius.

01:09 And then multiplied by delta t is a t final minus t initial.

01:13 The t final is zero degree celsius.

01:15 Initial would be negative 10.

01:21 So then we want to simplify that and then we can get the amount of energy that's required to heat the ice up to its melting point.

01:30 Then we want to determine the energy required to melt the 10 grams of ice.

01:35 So what we're going to do is take the heat of fusion of ice.

01:39 So heat of fusion is the amount of energy that is required to melt a certain mass of ice.

01:58 The equation that we're going to use is going to be q is equal to mass of the ice times delta h fusion.

02:18 So it's basically heat of fusion of ice.

02:22 So then if we do that, we end up with the end up with the end.

02:27 Energy required to heat to melt 10 grams of the ice.

02:30 So this is to make phase change occur.

02:34 Then, after that, the melted ice is going to be heated from 0 degrees celsius to an unknown temperature.

02:42 So set up another q equals mc delta t, but this time use the specific heat of water, 4 .184 joules per gram times degrees celsius.

02:52 The unknown temperature is going to be x, so that's t final, and t initial will be zero, because we're heating it up right after it melts.

03:01 Then shut up an equation, showing the cooling of hot water to the unknown temperature, t -final...

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