Advertisements
Advertisements
प्रश्न
Consider the situation of the previous problem. Assume that the temperature of the water at the bottom of the lake remains constant at 4°C as the ice forms on the surface (the heat required to maintain the temperature of the bottom layer may come from the bed of the lake). The depth of the lake is 1.0 m. Show that the thickness of the ice formed attains a steady state maximum value. Find this value. The thermal conductivity of water = 0.50 W m−1°C−1. Take other relevant data from the previous problem.
उत्तर
Let the point upto which ice is formed is at a distance of x m from the top of the lake.
Under steady state, the rate of flow of heat from ice to this point should be equal to the rate flow of heat from water to this point.
Temperature of the top layer of ice = −10°C
Temperature of water at the bottom of the lake = 4°C
Temperature at the point upto which ice is formed = `((DeltaQ)/(Deltat))_{ice} = ((DeltaQ)/(Deltat))_{water}`
`k_{ice}/(x/(Axx10)`= `K_{water}/((1-x)/(Axx4)`
`(1.7 xx 10)/x = (0.5xx4)/(1-x)`
`(1.7)/x = (0.5xx4)/(1-x)`
17 - 17x = 2x
`⇒ x =17/19 = 0.89 m`
`⇒ x = 89 cm`
APPEARS IN
संबंधित प्रश्न
Water is used as a cooling agent.
Give reason of Ice floats on water.
Answer the following:
On what basis and how will you determine whether air is saturated with vapour or not?
Calculate the time required to heat 20 kg of water from 10°C to 35°C using an immersion heater rated 1000 W. Assume that 80% of the power input is used to heat the water. Specific heat capacity of water = 42000 J kg−1 K−1.
On a winter day the temperature of the tap water is 20°C whereas the room temperature is 5°C. Water is stored in a tank of capacity 0.5 m3 for household use. If it were possible to use the heat liberated by the water to lift a 10 kg mass vertically, how high can it be lifted as the water comes to the room temperature? Take g = 10 m s−2.
Draw a graph to show the variation in density of water with temperature in the range from 0°C to 10°C.
Explain, why does a glass bottle completely filled with water and tightly capped burst when placed in a freezer?
A deep pond of water has its top layer frozen. What will be the likely temperature of water layer at the bottom of the pond?
What are hot spots? How can you extract energy from a hot spot, if it does not come in contact with underground water?
What is the criterion of choosing the two metals for a bimetal strip?
Give reasons for the following:
Even when the water in the lakes is frozen, fish can survive.
When the temperature of water decreases below 4 °C it’s volume _______.
Write the name.
The instrument used to study anomalous behaviour of water.
Name the following diagram appropriately.
A graph between the volume and temperature of water is shown. Explain the anomalous behaviour of water.
