Heat Equation and numerical problems
Heat Equation:
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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