We
are solving series of problems based on the concepts of
thermodynamics. We also deal about calorimetry in this chapter which deals
about conversion of heat energy to other forms of energies and its applications
further. We do define terms like specific heat and latent heat to explain this
properties and they are the basic terms of heat concepts. When there is a
change in the temperature, we need to deal with specific heat concept and when
there is a change of state, we need to study it in terms of latent heat and
during this process, all the supplied heat energy is used to change the state
of the system and hence its temperature remains constant.
Problem
During
an adiabatic process,pressure of the gas is proportional to the cube of the
temperature and basing on that we need to find the ratio of specific heats of
the gas. Problem is as shown in the diagram below.
Solution
We
need to take the relation between pressure and temperature and taking that into
consideration with the given data, we can get the relation between pressure and
temperature in the adiabatic process and the problem can be solved as shown in
the diagram below.
Problem
A
metal sphere of known radius and specific heat is given to us and it is
rotating about its own axis with certain rotations per second. When it is
stopped half of its energy is converted into heat and we need to measure the
raise in the temperature of the system and the problem is as shown in the
diagram below.
Solution
As
the body is rotating it has rotational kinetic energy and half of it is
converted into heat energy as per the given problem. Taking law of conservation
of the energy, we can solve the problem as shown in the diagram below.
Problem
The
relation between internal energy,pressure and volume is given to us as shown in
the diagram below. We need to find the ratio of specific heats and some
constants are also available in the problem.
Solution
We
need to differentiate the given equation to get the change in internal energy
and hence it can be expressed in terms of specific heat of the gas at constant
volume. Problem can be further solved as shown in the diagram below.
Problem
Work
done by a system under isothermal conditions has to be determined that change
its volume from one to other and satisfy the given equation. Problem is as
shown in the diagram below.
Solution
Relation
of pressure with other physical quantities is given to us as shown in the
diagram below. We need to measure the work done and the pressure is not
constant here. So to get the work done we shall integrate the pressure with the
change in the volume as shown in the diagram below. By simplifying the equation
further, we can get the solution as shown in the diagram below.
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