How much heat is required to raise a 770-g copper pan from 14^∘ C to 90^∘ C if (a) the pan is em

How much heat is required to raise a 770-g copper pan from...

How much heat is required to raise a $770-\mathrm{g}$ copper pan from $14^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$ if (a) the pan is empty or contains (b) $1.1 \mathrm{~kg}$ of water and (c) $4.2 \mathrm{~kg}$ of mercury?

Key Concepts

Calorimetry

Calorimetry is the study of heat transfer during physical and chemical processes. It involves measuring the amount of heat absorbed or released by substances as their temperatures change, which is fundamental in determining energy requirements in heating or cooling scenarios.

Specific Heat Capacity

Specific heat capacity is a material property that indicates the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. It plays a central role in calculating heat energy changes in systems, as different substances require different amounts of energy for the same temperature change.

Heat Energy Calculation

The calculation of heat energy involves using the formula q = m × c × ?T, where q represents the heat energy absorbed or released, m is the mass of the substance, c is its specific heat capacity, and ?T is the change in temperature. This equation is vital for determining how much heat energy is needed to achieve a particular temperature change in a substance.

Transcript

00:01 In this problem, we're considering a copper pan with a mass of 770 grams.

00:08 And we want to raise its temperature from an initial temperature of 14 degrees celsius to a final temperature of 90 degrees celsius.

00:20 In part a, we're considering that the pan is empty.

00:26 And if the pan is empty, in order to raise its temperature, we just need to raise it.

00:31 Raise the temperature of the metal copper pan itself.

00:37 So the energy needed to raise the temperature is equal to mass times specific heat times the change in temperature.

00:47 So we can look up the specific heat of copper in a table and find that it is 386 joules per kilogram kelvin.

00:59 And of course, if we're going from 14 ,000, 13 degrees celsius to 90 degrees celsius.

01:06 The change in temperature there is going to be 76 degrees celsius or 76 kelvin.

01:13 Now it's just a matter of plugging in the numbers.

01:17 You would plug in 0 .77 kilograms for m, 386 joules per kilogram kelvin for c, and 76 kelvin for delta t.

01:32 That a total of about 22 .6 kilojoules is needed to raise the temperature when the pan is empty.

01:44 In part b, we're considering that the pan is filled with 1 .1 kilograms of water.

01:57 The process is going to be the same, but we don't need to only increase the temperature of the pan, we also need to increase the temperature of the water...

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