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Cryobiology

Heat transfer problems

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Heat transfer by conduction

Heat transfer (Q) by Conduction formula is given by

Where k is the thermal conductivity of the material,

A is the cross sectional area,THot is the higher temperature,

TColdis the cooler temperature,

t is the time taken,

d is the thickness of the material.

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Heat transfer by Convection

Heat transfer by Convection is given by

Where Hcis the heat transfer coefficient,

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Heat transfer by radiation

The Heat transfer by radiation is given by

Here is the Stefan Boltzmann Constant = 5.670373 10-8kg s-3K-4

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Question 1:

A room is maintained at 20oC where as temperature outside the room is

10oC. There is one of the window in the corner having area 1m by 2m.

Calculate the heat transfer?

Thermal Conductivity of glass is 1.4 W/mK.

Tips:

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Question 2:

Calculate the Heat lost by the block when iron block decreases its

temperature from 60oC to 40oC if the mass of the body is 2 Kg.

Specific heat of iron C = 0.45 kJ/kg K.

Tips:

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Question 3:

Calculate the heat required to raise 0.6 Kg of sand from 30oC to 90oC?

(Specific Heat of sand = 0.08 J/KgoC)

Tips:

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Question 4:

Calculate the temperature difference if 50 Kg of water gains 500 K J of

heat?

Specific Heat of water = 4.2 103J/KgoC

Tips:

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Question 5:

Calculate the specific heat capacity of given copper of mass 75 g and

temperature difference 10oC if 200 J of heat is lost?

Tips:

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Question 6:

Calculate the heat capacity if 2000 J of heat is

used to heat iron rod of mass 5 Kg from 20oC

to 30oC?

Tips:

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Question 7:

Calculate the temperature if 100 J of heat is released by the body of mass 5

Kg having specific heat of 0.5 J/KgoC?

Tips:

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Question 8:

Calculate the heat released when the temperature changes by 50oC by a

body of mass 4 Kg having specific heat of 0.04 J/kgoC?

Tips:

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Question 9:

Find the final temperature of the mixture, if two cup of water having

masses m1=150g and m2=250g and temperatures T1= 30 C and

T2=75 Care mixed in an isolated system in which there is no heat lost. (

c water=1cal/g.C)

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Question 10:

Two matters have specific heat capacities c and 2c. If we give Q and 4Q

heat to these matters, changes in the temperatures of them become

equal. If the matter A has mass m, find the mass of matter B in terms of m.

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Newton's Law of Cooling Formula

The rate of loss of heat by a body is directly proportional to the

temperature difference between system and surroundings,provided the difference is small.

Where t is the time taken,T(t) is the temperature of the given body at time t,Tsis the surrounding temperature,Tois the initial temperature of the body,k is the constant

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Question 1:

The oil is heated to 60oC. It cools to 50oC after 6 minutes. Find the time

taken by the oil to cool from 50oC to 40oC (Surrounding temperature Ts=

25oC).

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Question 2:

Robin heats the water to 70oC. He waits for 10 min. How much would be the

temperature if k = 0.056 per min and surrounding temperature is 27oC.

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Latent Heat Formula

Q= mL

L = Q/m

Where,

L = Latent heat of the substance

Q = Amount of energy transferred for the Phase change

m = Mass of the substance

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Latent Heat Flux

It is denoted by Qewhen water evaporates, it removes significant

amounts of heat. The energy that is added to break the hydrogen bonds

to allow evaporation is removed by the water vapour. It can be

calculated with the help of Bulk Formula,

Qe= aLECLU10(qaqs)

Where,

a= Density Of air ( 1.2 kg/m3)

LE= Latent Heat of vaporization (2260 kJ/kg)CL= Bulk transfer coefficient (Stanton Number)

U10= Wind speed at 10 m

qa= specific Humidity at saturation

qs= specific Humidity of overlying air

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Latent heat

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Latent heat

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Question 1:

Find the amount of heat for melting the ice having mass 1.3kg at -10 C?

(Lfusion=3.3105joule/kg, cice=2.2X10

3j/kg.C)

Hints: Addition of two separate events

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Question 2:

Find the amount of heat for evaporating 2.8kg of water at 45 C?

(Lvaporization=2.3106joule/kg cwater=4190j/kg.C)

Hints: Addition of two separate events