Name: Molar Specific Heat Capacities of Gases
Uploaded: 2019-07-19
Duration: 10 min 31 s
Description: Do all gases have the same molar heat capacities? Are there certain criteria for determining molar specific heat capacities of gases? Watch the video to find...

Question

Derive the relation between coefficient of linear and volume expansion.

Accepted Answer

Three coefficients of thermal expansion are,

$α =$ coefficient of linear expansion

$β =$ coefficient of areal expansion

$γ =$ coefficient of volume expansion

let,

Original length $= l$
change in length $= ∆ l$
original volume $= V$
change in volume $= ∆ V$
initial volume $= l^{3}$
final volume $(V + ∆ V) = {(l + ∆ l)}^{3}$
change in volume=final volume-initial volume

$∆ V = l^{3} + {(∆ l)}^{3} + 3 l \times (∆ l) (l + ∆ l) - l^{3} ∆ V = {(∆ l)}^{3} + 3 l \times (∆ l) (l + ∆ l)$
$∆ l^{3} a n d 3 l \times {(∆ l)}^{2}$ is neglected because it is too small

$∆ V = 3 l^{2} \times (∆ l)$
we know that
coefficient of volumetric expansion

$γ = \frac{∆ V}{V} \times ∆ t γ = \frac{3 l^{2} \times (∆ l)}{l^{3}} \times ∆ t γ = \frac{3 (∆ l)}{l} \times ∆ t γ = 3 α (\sin c e, \frac{∆ l}{l} \times ∆ t = α)$

Derive the relation between coefficient of linear and volume expansion.

Important Questions on Thermal Properties of Matter

Learn and Prepare for any exam you want !