why does temperature T1 drop rapidly than t1 thermometer i n hope's apparatus which phenomena is studied explain it.
Answers
Explanation:
(C) The initial temperature of water in the vessel is maintained at 10
∘
C. Due to freezing at the center, the temperature of water begins to fall. The water contracts and its increases.
(e) As the density of water increases, the cold water goes to the bottom of the vessel and the temperature of the waterfalls to 4
∘
C
(a) as shown by the lower thermometer and this remains constant.
( d) The temperature of water at the center falls below 4
∘
C, then the water expands instead of contracting, so, that its density decreases, therefore the water below 4
∘
C goes to the upper portion
(f) The temperature of waterfalls till 0
∘
C, as shown by the upper thermometer.
(b) Water at 0
∘
C freezes into ice and a layer of ice is formed at the top surface because the density of ice is less than that of water.
(g) Being a bad conductor of heat, ice prevents the loss of heat from the water below it to the surroundings.
Answer:
Goal of experiment
The goal of this experiment is to demonstrate that between the temperatures 0 °C and 4 °C, the density of water increases with increasing temperature. (To be exact: we are going to demonstrate that water has a higher density at 4 °C than at 0 °C.)
Theory: thermal volume expansion of liquids
The volume of liquids is, similarly to solids and gases, dependant on their current temperature. Liquids (with the exception described below) increase their volume with increasing temperature; the increase of their volume ΔV is, with some neglect, directly proportionate to increase of temperature Δt and the initial volume V0. This relation can be mathematically denoted as
ΔV≐βV0Δt,(1)
where the constant β describes the volumetric thermal expansion coefficient and is a characteristic property of every liquid. (The neglect mentioned above limits the validity of this relationship to “small” differences in temperature, where βΔt≪1.). The volume of the liquid V after heating is therefore equal to the sum of its initial volume Vo and the growth ΔV given by relationship (1):
V≐V0+βV0Δt=V0(1+βΔt).(2)
Relationship (2) can be expanded using mass and density:
mρ≐mρ0(1+βΔt),(3)
which can be simplified to:
ρ≐ρ01+βΔt.(4)
The result is logical and predictable – if the volume of a liquid increases with increasing temperature, its density (while conserving mass) necessarily decreases.
Theory: anomaly of water
The constant β used in the relationships above is itself dependent on temperature; this dependence is usually very small. In the case of water, however, β has negative values in the narrow range between 0 °C and 4 °C. Heating water inside this interval therefore leads to a decrease in volume, or an increase in density. This phenomenon, unobserved in other liquids, is often referred to as the anomaly of water.
The volume of water is then apparently minimal (and the density maximal) at approx. 4 °C; exceeding this temperature leads to the values of β becoming positive again and a subsequent increase in temperature causes an increase in volume (decrease in density), in agreement with the general theory.
The dependence of (distilled) water on temperature is illustrated by Fig. 1.
Fig. 1: Temperature dependance of desity of distilled water