We
are solving series of problems based on the concept thermodynamics. The topic
deal with the heat energy and its transformation into other forms of energies.
To study thermodynamics, we need to consider some fundamental quantities and
they are called coordinates of thermodynamics. Pressure, temperature,volume,
internal energy and entropy are some of the parameters called coordinates of
thermodynamics. Internal energy is the energy in side the system because of
molecular motion and it can not be measured absolutely. We can only measure the
change in the internal energy but not its absolute value. We have zeroth, first
and second law of thermodynamics to understand it. To deal with the conversion
of energy, we deal with a topic called calorimetry. According to principle of
calorimetry, when there is no transmission loss of heat in any form, heat lost
by hot body that is contact with the other body, heat gained by the cold body.
Problem
In
a thermodynamic process, pressure of the system is kept constant. In this
process 20 joule of heat is released and 8 joule of work is done on the gas. If
the initial internal energy of the gas is 30 joule, we need to find the final
internal energy of the system and the problem is as shown in the diagram below.
Solution
We
need to use first law of thermodynamics to solve this problem. As per it the
total heat energy supplied to a system is the sum of change in the internal
energy and the external work done by the system. Heat given to the system shall
be taken as positive and heat given by the system shall be treated as negative.
Work done by the system shall be treated as positive and vice versa. Taking the
notation into consideration, we can solve the problem as shown in the diagram
below.
Problem
It
is given in the problem that 70 calorie of heat energy is required to raise the
temperature of the two moles of gas at constant temperature at constant
pressure. If the same has to be done at constant volume, we need to know the
required heat energy and the problem is as shown in the diagram below.
Solution
We
need to know the definitions of specific heat of gas at constant volume and
pressure and we can get the value of heat required in both the cases. In the
case constant pressure, we need to supply heat energy to change internal energy
and to do some external work. By using the relation between specific dates, we
can solve the problem as shown in the diagram below.
Problem
A
block of ice falls from a height and it completely melts. If only three by
forth of heat energy is retained by the block then we need to find the height
from which the block has to fall from the given data.
Solution
We
need to use conservation of energy to solve this problem. When it is falling
from a certain height, it has potential energy and by the time it hits the
ground, its energy is converted into heat and gets converted into water. The
heat energy value can be obtained basing on the definition of latent heat. Taking
that into consideration, we can solve the problem as shown in the diagram
below.
Problem
A
bullet just melts when stopped by a obstacle. Assuming that only one quarter of
the total energy is absorbed by the obstacle, we need to find the velocity of
the bullet. Problem with standard data is as given in the diagram below.
Solution
As
the bullet is moving, it has kinetic energy and that is used to raise the
temperature of bullet until it melts and then the remaining heat energy is used
to melt itself. Substituting the data, we can measure the heat energy required
for this process. Equating that heat into work and kinetic energy, we can solve
the problem as shown in the diagram below.
Problem
If
two moles of mono atomic gas at T temperature is mixed with four moles of
another mono atomic gas at different temperature, we need to find the resultant
temperature of the mixture and the problem is as shown in the diagram below.
Solution
We
can equate the total heat energy of both the gas sets as the heat energy of the
combination and solve the problem as shown in the diagram below.
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