Q. The apparent expansion of 50cc of a liquid being heated through 20degree celcius is found to be .5 cc the coefficient of linear expansion of the container

-5

0.9x 10 .the coefficient of absolute expansion of the liquid is?

To find the coefficient of absolute expansion of the liquid, we need to consider both the expansion of the liquid itself and the expansion of the container holding it. The coefficient of absolute expansion of a liquid can be calculated using the formula that relates the volume change of the liquid to the volume change of the container. Let's break this down step by step.

Understanding the Problem

We have the following information:

• Volume of the liquid (V) = 50 cc
• Temperature change (ΔT) = 20 °C
• Apparent expansion of the liquid = 0.5 cc
• Coefficient of linear expansion of the container (α_container) = 0.9 x 10^-5 °C^-1

Key Concepts

The coefficient of volume expansion (β) for a liquid is defined as the change in volume per unit volume per degree change in temperature. The formula for the apparent expansion of the liquid can be expressed as:

Apparent Expansion = Actual Expansion - Expansion of the Container

Calculating the Actual Expansion

First, we need to calculate the expansion of the container. The volume expansion of the container can be determined using the linear expansion coefficient:

Volume Expansion of Container = V × 3 × α_container × ΔT

Substituting the values:

Volume Expansion of Container = 50 cc × 3 × (0.9 x 10^-5 °C^-1) × 20 °C

Volume Expansion of Container = 50 × 3 × 0.9 x 10^-5 × 20

Volume Expansion of Container = 50 × 3 × 0.9 × 20 x 10^-5

Volume Expansion of Container = 50 × 54 x 10^-5 = 2700 x 10^-5 cc = 0.027 cc

Finding the Actual Expansion of the Liquid

Now, we can find the actual expansion of the liquid using the apparent expansion:

Actual Expansion = Apparent Expansion + Expansion of the Container

Actual Expansion = 0.5 cc + 0.027 cc = 0.527 cc

Calculating the Coefficient of Absolute Expansion

Finally, we can calculate the coefficient of absolute expansion (β) of the liquid using the formula:

β = Actual Expansion / (V × ΔT)

Substituting the values:

β = 0.527 cc / (50 cc × 20 °C)

β = 0.527 / 1000 = 0.000527 °C^-1

Final Result

Thus, the coefficient of absolute expansion of the liquid is approximately 5.27 x 10^-4 °C^-1.