Answer to Question #161003 in Mechanics | Relativity for Ermus Ken

Question

1. What is the density of water at 4°C?

2. Does the water density change?

3. What is the density of Gold?

4. Does the Gold density change?

Answer 1

Solution:

Density water versus temperature:

+100°C    958.4 $(\frac{kg}{m^3})$

+80°C     971.8 $(\frac{kg}{m^3})$

+60°C     983.2 $(\frac{kg}{m^3})$

+40°C     992.2 $(\frac{kg}{m^3})$

+30°C     995.6502 $(\frac{kg}{m^3})$

+25°C     997.0479 $(\frac{kg}{m^3})$

+22°C     997.7735 $(\frac{kg}{m^3})$

+20°C     998.2071 $(\frac{kg}{m^3})$

+15°C     999.1026 $(\frac{kg}{m^3})$

+10°C     999.7026 $(\frac{kg}{m^3})$

+4°C      999.9720 $(\frac{kg}{m^3})$

 0°C      999.8395 $(\frac{kg}{m^3})$

−10°C     998.117 $(\frac{kg}{m^3})$ (super cooled)

−20°C     993.547 $(\frac{kg}{m^3})$ (super cooled)

−30°C     983.854 $(\frac{kg}{m^3})$ (super cooled)

the density of gold: 19.30 $(\frac{g}{cm^3})$ or 19300 $(\frac{kg}{m^3})$ at 25ºC metals density vs temperature is linear and can be calculated from the volume temperature expansion coefficient since mass is fixed, density is inversely proportional to volume, which in this case, goes up by 42.6*10^-6 per ºC. So density at 125ºC, for example, goes down by a factor of 1 + 100•42.6*10^-6 or 1+42.6*10^-4 or 1.00426, which means density at 125ºC is $\dfrac{19.3}{1.00426}=19.22\;(\frac{g}{cm^3})$ ,so density at 4ºC, goes up by a factor of 1 + 21•42.6*10^-6 which is 19.30, same number to the accuracy allowed by the date. Gold linear expansion coefficient is 14.2*10^-6 and volume expansion coefficient is 42.6*10^-6