# Columns of liquids at different temperuatures

1. May 15, 2006

### Amith2006

Sir,
# A vertical column of liquid 50 cm long at 50 degree Celsius balances another column of same liquid 60 cm long at 100 degree Celsius. What is the coefficient of absolute expansion of the liquid?
I solved it in the following way:
Pressure exerted by 50 cm of liquid at 50 degree Celsius = Pressure exerted by 60 cm of liquid at 100 degree Celsius.
Hence, (h1)(d1)g = (h2)(d2)g
50 x d1 x g = 100 x d2 x g
d1 = 2 x d2 -------- (1)
We know that d1 = d2[1 + r(dt)] --------- (2)
Where d1 = density at T1 temperature
d2 = density at T2 temperature(Here T1<T2)
r = coefficient of cubical expansion of the liquid
dt = T2 – T1
Substituting (1) in (2) we get,
2 x d2 = d2[1 + (r x 50)]
By solving we get,
r = 0.004 / deg Celsius

2. May 16, 2006

### Amith2006

3. May 16, 2006

### Gokul43201

Staff Emeritus
h2=60 (not 100) cm

4. May 17, 2006

### Amith2006

Though I typed it wrongly, I solved it by using h2 = 60cm. Is it right?

5. May 17, 2006

### Andrew Mason

The problem here is that the change in volume is significant. So the rate of change in volume increases as the volume and temperature increase, does it not? It is a little more complicated than simple linear expansion.

AM

Last edited: May 17, 2006
6. May 20, 2006

### Gokul43201

Staff Emeritus
Amith, you need to use :

$$\gamma = \frac{1}{V} \frac{\partial V}{\partial T}$$

This is the definition of volumetric thermal expansion coefficient.