3a. A heat engine performs a Carnot cycle which generates 100 kJ of net work and takes in 400 kJ of heat. The gas isothermally expands at a temperature which is 100C higher than the temperature at which the gas is isothermally compressed. By how much is the entropy of the gas changed during isothermal expansion?

b. A tape measure is made of a particular material which has a linear thermal expansion coefficient of 20 10^6 K1. At -10C, using it you measure a piece of the material (which has a linear thermal expansion coefficient of 80 10^6 K1) to have a length of 10 m. What length would the tape measure say the piece of material has at 30C? Assume the tape measure if marked to the mm level, and give your answer to that level of accuracy.

c. A solid wall made of a particular material passes heat by thermal conduction five times faster than a wall of the same total thickness which consists of three equal-thickness layers, the outer two being the same material as the first wall and the middle material being an unknown insulator. How many times lower is the thermal conductivity of the unknown insulator compared to the other material?