# Homework Help: Thermodynamics question: density, linear expansion and temp

1. Apr 1, 2015

### Patricia Reid

An object has a density of 1250 kg m3 at 10C and a coefficient of linear expansion of α = 2.5 × 10−5 1 /K . What is the object’s density when the temperature is 25C?

I have tried using the equation ΔL=αL° ΔT but this equation has nothing to do with density.

Your help would be greatly appreciated!

2. Apr 1, 2015

### uselesslemma

This is a volume mass density, which should have units of mass / volume. The expansion of the object is not restricted to one dimension.

This is not true. Any change in dimensions will be accompanied by a change in density. Why is this? Is the object's mass changing? How are density and volume related? Is there an equation that fits better for a change in volume?

Good luck.

3. Apr 1, 2015

### Patricia Reid

Ok thanks! So you could use the equation β=3α and then use the volume expansion formula. The equation that relates density to volume is ρ=M/V... but you don;t know what the mass is.

4. Apr 1, 2015

### uselesslemma

Did you try expressing the volume expansion formula in terms of ρ instead of V? You should find a result that is independent of the object's mass.

5. Apr 1, 2015

### Patricia Reid

[QUO TE="uselesslemma, post: 5061484, member: 542831"]Did you try expressing the volume expansion formula in terms of ρ instead of V? You should find a result that is independent of the object's mass.[/QUOTE]

Ok so you go....
V=3αVΔT
=3αΔTM/ρ
=3(2.5*10-5)(298-283)M/1250
=9.0*10-7M

Am I on the right track?

6. Apr 1, 2015

### uselesslemma

Check the correctness of this equation by comparing to the one you provided for linear expansion. V should not cancel algebraically...otherwise how would you find ρ?

7. Apr 2, 2015

### Patricia Reid

So I ended up using the equation V=(1+β(Tf-Ti)) Vi and substituting v=m/ρ which gave me the right answer!

8. Apr 2, 2015

### forceanger

Why did you do "1+" in your formula?

9. Apr 2, 2015

### Patricia Reid

I'm not really sure.... it was on a sheet my professor handed out it's suppose to be a parametrization for the volume or something it should have actually have been written as V(T)≈(1+β(Δt))V0

10. Apr 2, 2015

### Staff: Mentor

This looks correct to me.

Chet