Inconsistency of Carnot Principle and Second Law of Thermodynamics

We know that internal energy of an ideal gas is a state function and it solely depends on the temperature of the gas. The temperature of the gas can be changed by many ways. We can change it by compressing the gas or by supplying the heat from outside or by injecting more molecules into a given volume of the gas. We know that Carnot principle is based on the temperature difference of thermal reservoirs and their thermal capacities. Due to different ways of production of heat the temperature difference between two thermal reservoirs can be created in different ways. There are many ways for creating such temperature gradients. One way is to pump the heat from one reservoir to another reservoir by the means of an ideal heat pump. Second way is to heat up one reservoir by burning some sort of fuel. Third way is to heat up one reservoir by stirring its fluid or by passing electric current through it whatever the medium may be. In the fourth way we can compress one reservoir made up of gas and can expand the second reservoir of the gas simultaneously as happens in sound waves. From all of these four methods of creating temperature differences, first and fourth methods are striking and this lead to a very interesting result. This result is that Carnot principle and second law of thermodynamics are not consistent.