## Wednesday, January 11, 2017

### Thermodynamics Problems with Solutions One

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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