Find the time in which a layer of ice 3cm thick on the surface of pond will increase by 2mm when the temperature of air is –25°C. Take density of ice 900kg/m³and thermal conductivity 0.005cal/msK.

Solution

Initial thickness of layer of ice, x₁ = 3 cm
Final thickness of ice, x₂ = 3.2 cm
Temperature of air, $straight theta$ = -25^o C
Density of ice, $straight rho$ = 900 kg/m³Thermal conductivity, K = 0.005 cal/msK
Time taken to freeze the lake from thickness to x₁ is given by,
$straight t space equals space fraction numerator ρL over denominator 2 Kθ end fraction left parenthesis straight x subscript 2 squared space minus space straight x subscript 1 squared right parenthesis thin space straight t space equals space fraction numerator 0.9 cross times 80 over denominator 2 cross times 0.005 cross times 25 end fraction open square brackets left parenthesis 3.2 right parenthesis squared minus left parenthesis 3 right parenthesis squared close square brackets space space space equals fraction numerator 90 cross times 80 over denominator 25 end fraction open square brackets left parenthesis 3.2 right parenthesis squared minus left parenthesis 3 right parenthesis squared close square brackets space space space space equals space 357.12 space straight s$

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

Find the time in which a layer of ice 3cm thick on the surface of pond will increase by 2mm when the temperature of air is –25°C. Take density of ice 900kg/m³and thermal conductivity 0.005cal/msK.

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Is there any relation between uniform circular motion and simple harmonic motion?

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Write down the expression for the instantaneous velocity and acceleration of particle vibrating in simple harmonic motion.

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Where will the particle executing simple harmonic motion have acceleration maximum and speed zero?

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Mechanical Properties Of Fluids

Find the time in which a layer of ice 3cm thick on the surface of pond will increase by 2mm when the temperature of air is –25°C. Take density of ice 900kg/m3and thermal conductivity 0.005cal/msK.

Some More Questions From Mechanical Properties of Fluids Chapter

Is there any relation between uniform circular motion and simple harmonic motion?

What is periodic motion?

Write down the expression for the instantaneous velocity and acceleration of particle vibrating in simple harmonic motion.

How do you define the mean position of particle executing simple harmonic motion?

Define amplitude.

What is the net displacement of the particle executing simple harmonic motion in one complete oscillation?

Are all the periodic motions simple harmonic?

Does the time period of particle vibrating in simple harmonic motion depend upon its displacement?

Where will the particle executing simple harmonic motion have acceleration maximum and speed zero?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the time in which a layer of ice 3cm thick on the surface of pond will increase by 2mm when the temperature of air is –25°C. Take density of ice 900kg/m³and thermal conductivity 0.005cal/msK.