Heat Equation and numerical problems

 Heat Equation:


It is Experimentally proven that the amount of heat gain or the heat lost is directly proportional to

i) Mass of the body(m) and

ii) Change in temperature(dt)

From the statements,

           Q is directly proportional to (m)----------(1)

           Q is directly proportional to temperature change(dt)-------(2)

From equation (1)and(2), we get,

            Q is proportional to (m.dt)

        or, Q = m.s.dt

              where 's' is constant , and it means the specific heat capacity of the substance. Q = m.s.dt , is the required expression for the heat equation.

Why does the specific heat capacity of different objects differ:

Due to the weight and nature of different molecules , specific heat capacity of the different substances is different . Lighter substances contain more particles for a given weight . If all the particles are heated evenly ,lighter substances will absorb more heat because there are more particles in per unit mass. Not only this, due to the different nature of molecules, the intensity of the vibration of molecules becomes different if equal amount of heat energy is given to them. Hence, different substances have different heat capacities.

Q) An iron ball of 4 kg mass is cooled from 20 degree Celsius temperature to 10 degree Celsius. What amount of heat is released? The specific heat capacity of iron is 460 J/Kg degree Celsius.

Solution :

Here, Given:

Mass of the iron ball(m) = 4 kg

Initial temperature of the iron ball (t) = 20 degree Celsius

Final temperature of iron ball (T) = 10 degree Celsius

Specific heat capacity of iron (s) = 460 J/kg degree Celsius

Amount of heat released(Q) = ?

We know that ,

                            Q = m x s x {t - T}

                                = 4 x 460 x (20 - 10)

                                = 18400 J

Q) What amount of heat energy is required to increase the temperature  of 25 kg of water by 40 degree Celsius?

Solution :

Here, Given,

Mass of water (m) = 25 kg

Change in temperature (dt) = 40 degree Celsius

 Specific heat capacity of water (s) = 4200 J/kg degree celsius

Quantity of heat required (Q) = ?

We know that,

Q = m.s.dt

Q = 25 x 4200 x 40

Q = 4200 kJ

 

 

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