How Does Density Affect Calculations in Thermodynamics Problems?

[Blade]

I'm stumped on some of the thermodynamic problems involving density.

Heat a 1.0kg bar of lead at atmospheric pressure from 25C to 60C and find the work done by the lead. (density of lead = 1.13*10^4 kg/m^3)
The only equations I was given was the Ideal Gas Law... which lead is not a gas.. Someone also told me that apparently work=pressure*volume, which also doesn't help. Density is molar mass/volume (I think), which does nothing in this case, since I basically already can determine both those components. Where do I start?

[Answer=.02729J]

A droplet of silver has a radius of .6mm. How many silver atoms are in the droplet. The density of silver is 1.05*10^4 kg/m^3
This sounds simple, but I must be missing a conversion. I'm sure I'm suppose to multiply something by Avogradro's number, but not sure how to get the info from the density and radius.

(Answer=5.3*10^19 atoms)

 

[ShawnD]

Heat a 1.0kg bar of lead at atmospheric pressure from 25C to 60C and find the work done by the lead. (density of lead = 1.13*10^4 kg/m^3)
The only equations I was given was the Ideal Gas Law... which lead is not a gas.. Someone also told me that apparently work=pressure*volume, which also doesn't help. Density is molar mass/volume (I think), which does nothing in this case, since I basically already can determine both those components. Where do I start?

[Answer=.02729J]

I'm thinking you would need the coefficient for linear expansion for the lead. Then you would have the change in volume. Since the pressure is N/m^2. If you multiply the pressure by the change in volume (m^3), you get Nm which is J.

A droplet of silver has a radius of .6mm. How many silver atoms are in the droplet. The density of silver is 1.05*10^4 kg/m^3
This sounds simple, but I must be missing a conversion. I'm sure I'm suppose to multiply something by Avogradro's number, but not sure how to get the info from the density and radius.

(Answer=5.3*10^19 atoms)

find volume:
v = (4/3)[tex]\pi[/tex]r^3
v = (4/3)[tex]\pi[/tex](0.0006)^3
v = 9.0478*10^-10 m^3

find mass:
(9.0478*10^-10 m^3) * (1.05*10^4 kg/m^3) = 9.5*10^-6 kg = 0.0095g

use molar mass to find mols:
0.0095g * 1mol/107.87g = 8.807*10^-5 mols

use avogadro's number to find atoms:
8.807*10^-5 mols * 6.02*10^23 atoms/mol = 5.30185*10^19 atoms


Yep, still got it

 

[M98Ranger]

Hi there,

I can understand how thermodynamics problems involving density can be challenging. Let me try to break it down for you.

First, let's review the definition of density. Density is the mass of a substance per unit volume. In other words, it is how much matter is packed into a certain amount of space. The equation for density is:

Density = Mass/Volume

Now, let's look at the first problem given. We have a 1.0kg bar of lead that is being heated from 25C to 60C. To find the work done by the lead, we need to use the equation:

Work = Pressure * Change in Volume

But wait, we don't have the change in volume. However, we do know that the density of lead is 1.13*10^4 kg/m^3. Using the definition of density, we can rearrange the equation to solve for volume:

Volume = Mass/Density

Since the mass is given as 1.0kg, we can plug that in along with the density to find the volume of the lead bar at 25C. Then, using the Ideal Gas Law (PV=nRT), we can find the volume at 60C. The change in volume will give us the value we need to calculate the work done by the lead.

Now, for the second problem, we have a droplet of silver with a given radius and we need to find the number of silver atoms in it. First, we need to calculate the volume of the droplet using the formula for the volume of a sphere:

Volume = (4/3) * π * radius^3

Once we have the volume, we can use the density of silver to find the mass of the droplet. Then, using the molar mass of silver (107.87 g/mol), we can convert the mass to moles. Finally, we can use Avogadro's number (6.022*10^23) to find the number of atoms in the droplet.

I hope this helps guide you in solving these problems. Remember to always review the definitions and equations involved in thermodynamics and think about how they can be applied in each scenario. Good luck!