Expansion of Liquid and Gas

Expansion of Liquid

• In case of liquid linear and superficial expansivities are absent.
• Liquid is heated in a vessel which expand itself so the expansion that we observe is called apparent expansion.
• Apparent expansion is always less than real or absolute expansion due to expansion of vessel.

1. Coefficient of apparent expansion or apparent expansivity (${\gamma }_a$)

• • The apparent change in volume per unit original volume per degree change in temperature is called apparent expansivity.
  • ${\gamma }_a=\frac{(\Delta V{)}_a}{V\Delta \theta }$ or $(\Delta V{)}_a$ =$V{\gamma }_a\Delta \theta$

1. Coefficient of real expansion or real expansivity (${\gamma }_r$)

• • Real change in volume per unit original volume per degree change in temperature is called real expansivity. It is constant for a liquid.
  • ${\gamma }_r=\frac{(\Delta V{)}_r}{V\Delta \theta }$ or $(\Delta V{)}_r$ =$V{\gamma }_r\Delta \theta$

Now,

Real expansion = Apparent expansion + Expansion of vessel.

or, ${\gamma }_r={\gamma }_a+{\gamma }_g={\gamma }_a+3{\alpha }_g$

Where, ${\gamma }_g$=Cubical expansivity of vessel.

Note:

• A vessel completely filled by liquid is heated then volume of liquid overflow or on cooling volume of empty space above liquid is

$(\Delta V)a$ =$V_o{\gamma }_a\Delta \theta$

• A liquid is placed in a vessel upon certain mark so that level of liquid remain at same mark at all temperature then,

$(\Delta V)l=(\Delta V)g\to {\gamma }_r={\gamma }_g=3{\alpha }_g$

• Liquid is placed in a vessel so that volume of empty space above liquid remain same at all temperature then,

$(\Delta V{)}_t$=$(\Delta V{)}_r$$\to$ $V_r{\gamma }_r=V_g{\gamma }_g$

Change in density

• When temperature is increased, the volume of the constant mass also increase and hence the density decrease.

• .${\rho }_{\theta }=\frac{{\rho }_o}{1+\gamma \Delta \theta }$

Dulong and Petit's Experiment

• When $h_{\theta }$and $h_o$be the height of liquid column in two sides of U shaped tube at $\theta °C$and $0°C$then,

Absolute expansivity ($\gamma$) = $\frac{h_{\theta }-h_o}{h_o\theta }$

• The height $h_{\theta }$- $h_o$is measured with a cathetometer or a travelling microscope mounted vertically.

• This experiment is done to find the real expansivity of the liquid.

Correction of Barometer

• When the height of barometer is observed $h_{scale}$ at $\theta °C$ then true height is given by

$h_{true}=h_{scale}(1+\alpha \theta )$, Where is linear expansivity of scale.

• The correct height is measured at $0°C$, then reading at $\theta °C$ is observed $h_{scale}$ then

$h_{correct}=h_{scale}[1-(\gamma -\alpha )\theta ]$

Anomalous Behavior of Water

• It is a different behavior of water where water expands on cooling from $4°C$ to $0°C$ and vice versa.

• Water has greatest density and least volume at $4°C$

• Water freezes from top of pond, which is an example of Anomalous Behavior. Existence of aquatic life on ice age was possible due to this behavior too.

• Expansivity of water is -ve from $0°C$ to $4°C$.

• Mean or average expansivity of water is 0 at $4°C$.

Expansion of Gas

Note:

For expansion of gas, study the topic "Gas Laws".