## Thursday, January 12, 2017

### Thermodynamics Problems with Solutions Four

We are solving series of problems based on the concept of thermodynamics. It is a branch of physics that deals with the heat energy conversion into other forms and its applications. Carnot engine is a ideal heat engine that converts the given heat into work under a cyclic process. As the process is cyclic process, internal energy remains same and all the supplied heat is going to be converted into work. But we know that heat is a disordered format of energy and it cannot be completely converted into work. That is the reason why, heat engine cannot have hundred percent efficiency. Heat engine will have three basic parts by name source, working substance and sink. Source do supply heat, working substance do convert the heat into work and the extra generated heat to the sink.

Problem

Pressure and volume graph for two different gases during adiabatic process is given to us as shown in the diagram below. We need to know which graph belongs to which gas.

Solution

From the pressure and volume graph, it can be found that the slope of the graph is directly proportional to the ratio of specific heats of the gas. It is clear from the graph that the slope of the second curve is more and hence it shall be the gas with more ratio of specific heat value. Solution of the problem is as shown in the diagram below.

Problem

A refrigerator is placed in a room of temperature of 300 kelvin and the system temperature is 264 kelvin. We need to measure the how many calories of heat shall be delivered to the room to the room for each kilo kelvin of energy consumed by refrigerator by the system ideally. Problem is as shown in the diagram below.

Solution

We know that proficiency of a refrigerator is the amount of work done when compared with the heat energy supplied to the system. It can also be expressed in terms of temperature as shown in the diagram and is solved as shown in the diagram below.

Problem

In carnot’s engine efficiency is 40 % for a certain temperature of the hot source. To increase the efficiency of the system by 50 %, what shall be the source temperature and the problem is as shown in the diagram below.

Solution

We know that the efficiency of heat engine is the magnitude of the work done when compared with the heat energy supplied and it can be expressed in terms of absolute temperature as shown in the diagram below.

We need to apply it for two cases and solve the problem as shown in the diagram below.

Problem

The relation between temperature and pressure is given to us for a certain gas and we need to find the specific heats ratio of that gas. Problem is as shown in the diagram below.

Solution

This process is adiabatic process and we need to write the given relation between pressure and temperature from the given format to the standard format so that we can solve and find the ratio of specific heats of the given gas as shown in the diagram below.

Problem

When a mono atomic gas expands at constant pressure, the percentage of the heat supplied that increases the temperature of the gas and in doing external work is how much is the problem and it is as shown in the diagram below.

Solution

We know that if volume is kept constant, work done is zero and corresponding specific heat is defined as per it and vice versa. When we write ratio of specific heats, it becomes the ratio of heat supplied to the change in the internal energy and internal energy change the temperature of the system. Thus we can find the percentage value basing on the specific heats ratio value as shown in the diagram below.