Q17 of 64 Page 12

The density of water at 0°C is 0.998 g cm–3 and at 4°C is 1.000g cm–3. Calculate the average coefficient of volume expansion of water in the temperature range 0 to 4°C.

Given:


Density of water at 0 °C: ρ0 = 0.998 g cm-3


Density of water at 4 °C: ρ4 = 1.000 g cm-3


Temperature Range: θ = 4 °C



Formula used:


We know that the formula for volume expansion is:



Where Vθ is the volume at θ °C


V0 is the volume at 0 °C


γ is the coefficient of volume expansion


Now, since


On substituting :







As density decreases γ = -5 x 10-4 ° C-1


Hence the average Calculate the average coefficient of volume expansion of water in the temperature range 0 to 4°C is


More from this chapter

All 64 →
15

A meter scale is made up of steel and measures correct length at 16°C. What will be the percentage error if this scale is used (a) on a summer day when the temperature is 46°C and (b) on a winter say when the temperature is 6°C? Coefficient of linear expansion of steel = 11 × 10–6 °C–1.

 16

A metre scale made of steel reads accurately at 20°C. In a sensitive experiment, distances up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel = 11 × 10–6 °C–1.

 18

Find the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are 12 × 10–6 °C–1 and 23 × 10–6 °C–1 respectively.

 19

A pendulum clock gives correct time at 20°C at a place where g = 9.800 m s–2. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where g = 9.788 m s–2. At what temperature will it give correct time? Coefficient of linear expansion of steel = 12 × 10–6 °C–1.