∙You add 8950 J of heat to 3.00 mol of iron. (a) What is the...

$\bullet$ You add 8950 J of heat to 3.00 mol of iron. (a) What is the temperature increase of the iron? (b) If this same amount of heat is added to 3.00 $\mathrm{kg}$ of iron, what is the iron's temperature increase? (c) Explain the difference in your results for parts (a) and (b).

Key Concepts

Heat Capacity

Heat capacity is the property of a substance that indicates the amount of heat required to change its temperature by a given amount. It is a fundamental concept in thermodynamics and is used to connect the energy supplied (or removed) to a system with its resulting temperature change. In problems involving heating, the heat capacity determines how much the temperature changes when a certain amount of energy is added or removed.

Specific Heat Capacity

Specific heat capacity is defined as the amount of heat required to raise the temperature of one gram (or one unit mass) of a substance by one degree Celsius. This property is particularly useful when dealing with masses of a substance, allowing one to calculate temperature changes from energy input on a per-mass basis.

Molar Heat Capacity

Molar heat capacity refers to the heat required to raise the temperature of one mole of a substance by one degree Celsius. It is essential when working with quantities given in moles, as it directly links the energy transferred to the temperature change per mole of the substance, instead of per unit mass.

Unit Conversion between Mass and Moles

In thermodynamics, converting between mass and moles is crucial because substances can be quantified by either mass or the number of particles. This conversion makes use of the molar mass of the substance and allows thermodynamic calculations to be carried out consistently, whether using specific heat capacity or molar heat capacity.

Transcript

00:01 Let's take over the question.

00:01 The question was asking us the changing temperature.

00:04 And we know the heat is equal to mass times specific heat times the changing temperature.

00:08 So the changing temperature is equal to q over mc.

00:12 Q is the heat.

00:14 M is the mass.

00:15 C is the specific heat.

00:17 And in this question, you were saying that there were three more irons in this question.

00:22 And when the model mass, the question is 55 .8 gram per more.

00:26 So the total mass will be 3 more times 508.

00:30 Gram per mole and then we'll give us 167 .4 grand and if we converted to a kilogram is 0 .1674 kilograms and the specific heat for the iron is 470 g.

00:43 Per kilogram times kelvin and the heat added to the iron is 8950 g u so now let's work out our calculations so we know that delta t is equal to q over mc so it's 890 jude, okay, let me see, 8 ,950 jule over the mass, which is 0 .1674 kilogram, okay, times the specific here, which is 470, jew over kilogram per kelvin.

01:40 And that will give us the delta t is equal to 113 .a kelvin.

01:48 Okay, so that's the changing temperature for this question.

01:53 Let's figure out the change of temperature for the next question.

01:56 So now the mass changed to 3 kilograms.

01:58 Rest is the same and still looking forward of changing temperature.

02:02 So we know the delta is equal to q over mc...

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