As a physicist, you put heat into a 500.0 -g solid sample at...

As a physicist, you put heat into a 500.0 -g solid sample at the rate of 10.0 $\mathrm{kJ} / \mathrm{mim}$ , while recording its temperature as a function of time. You plot your data and obtain the graph shown in Fig. 17.30 . (a) What is the latent heat of fusion for this solid? (b) What are the specific heats of the liquid and solid states of the material?

Key Concepts

Latent Heat of Fusion

Latent heat of fusion is the amount of energy required per unit mass to change a substance from a solid to a liquid at its melting point without a change in temperature. It is a crucial concept in understanding phase transitions where the energy is used to overcome intermolecular forces rather than increasing kinetic energy.

Specific Heat Capacity

Specific heat capacity is the amount of energy per unit mass required to raise the temperature of a substance by one degree Celsius (or Kelvin). It helps quantify the thermal response of a material in different phases, and in experiments, it is determined by measuring the temperature change under a known heat input.

Heating Curve Analysis

Heating curve analysis involves interpreting the changes in temperature over time as a substance is heated. The curve typically shows regions with constant slope where the temperature changes steadily, indicating sensible heating, while plateaus indicate phase transitions where latent heat is being absorbed.

Calorimetry

Calorimetry is the measurement of heat transfer during physical or chemical processes. It provides the framework for determining quantities like latent heat and specific heat by tracking how a substance’s temperature changes in response to a controlled heat input.

Transcript

00:01 In this problem, we're given a sample of material that's unknown.

00:04 We know that it is 0 .5 .00 kilograms.

00:11 And there's heat that is being put into this sample, and the heat's being put in at a rate of 10 .0 kilojoules per minute.

00:23 We're provided a graph, and the graph shows us that the sample goes from negative 5 degrees celsius to 10 degrees celsius in a time of one minute.

00:37 That's all the sample is solid, then the sample is going to melt, and it takes a time of 1 .5 minutes for the sample to melt.

00:50 That's the transition from solid to liquid.

00:55 And then after this happens, the sample goes from a temperature of 10 degrees celsius to 40, degrees celsius.

01:05 That again happens in a time of 1 .5 minutes.

01:11 We want to find the various constants that are associated with heating the sample in liquid phase, melting the sample, and heating the sample in solid phase.

01:22 So the specific heat of the sample hunt solid, we'll call this c s for c solid, is going to be equal to the rate we're putting heat in, so that's 10 .0 kilojoules per minute multiplied by how long we heated the sample for.

01:46 So that was one minute.

01:51 And we also need to multiply by how much it heated up by, divided by how much it weighed.

01:58 So that's going to be 15 degrees celsius divided by 0 .5 .00 kilograms.

02:11 Putting this all together, we'll find we have a specific heat of 1 .33 kilojoules per kilogram degrees celsius.

02:27 Or we could also express this in terms of joules as 1 .33 times 10 to the third joules per kilogram degree celsius.

02:41 That would be the specific heat, how much energy...

Please give Ace some feedback