Starting with an energy balance on a ring-shaped volume element, identify the two-dimensional steady heat conduction equation in cylindrical coordinates for T(r, z) for the case of constant thermal conductivity and no heat generation.

Ariver flows from north to south at 8 km/h. a boat is to cross this river from west to east at a speed of 20 km/h (speed of the boat with respect to the earth/ground). at what angle (in degrees) must the boat be pointed upstream such that it will proceed directly across the river (hint: find the speed of the boat with respect to water/river)? a 288 b. 21.8 c. 326 d. 30.2

Air is compressed isentropically from an initial state of 300 k and 101 kpa to a final temperature of 1000 k. determine the final pressure using the following approaches: (a) approximate analysis (using properties at the average temperature) (b) exact analysis

Prove the equivalence between the two statements of the 2nd law of thermodynamics (i.e., a violation of one statement leads to the violatio the other statement)