# When a liquid is heated in a copper vessel and a silver vessel, the apparent coefficient of...

## Question:

When a liquid is heated in a copper vessel and a silver vessel, the apparent coefficient of expansion is "C" and "S", respectively. If the coefficient of linear expansion of copper is "A", then what is the coefficient of linear expansion of silver?

## Thermal Expansion:

When a liquid kept in a container is heated, the temperature of both liquid as well as the container increases, which causes thermal expansion of the liquid as well as the container. The apparent coefficient of expansion of liquid is found by subtracting the coefficient of volume expansion of container from that of the liquid.

Given Data

• Apparent coefficient of volume expansion of liquid in copper vessel and silver vessel are C and S respectively
• Linear coefficient of expansion of copper as A

Finding the coefficient of linear expansion of Silver (B)

Let the coefficient of volume expansion of liquid be {eq}\beta{/eq}

The apparent coefficient of expansion of liquid in copper container is written as:

• {eq}C\ = \beta\ - 3\times A\ {/eq} ....equation-1

Similarly, the apparent coefficient of expansion of liquid in silver container is written as:

• {eq}S\ = \beta\ - 3\times B\ {/eq} ....equation-2

From equations-1 and 2:

• {eq}S\ = C\ + 3\times A\ - 3\times B\ {/eq}
• {eq}B\ = A\ +\dfrac{(C\ - S)}{3} {/eq} 