A horizontal cylindrical pipe (k = 10 W/m·K) has an outer diameter of 15 cm and a wall thickness of 5 cm. The pipe is situated in a stationary air, where the air and surrounding temperature is 27°C. The outer surface temperature of the pipe is 127°C, and the pipe surface has an emissivity of 0.5. Determine the inner surface temperature of the pipe. Use the following air properties for the analysis:
k = 0.03 W/m∙K, ν = 20.92 × 10−6 m2 /s, α = 29.90 × 10−6 m2 /s, Pr = 0.70

Agas mixture with a compostion of 55 methane, 30% propane, and 15 butane by volume) is compressed from 1 bar and 25°c to 9bar in a compressor with an isentropic efficiency of 85%. the environment has a temperature of to25 c. determine (a) the exit temperature of the mixture (b) the specific work required to run the compressor (c) the specific entropy generation of the process (d) the specific exergy destruction of the process (e) the second law efficiency of the compressor