Why we use the lagrange Equation?

Apipe with an outside diameter of 15 cm is exposed to an ambient air and surrounding temperature of -20°c. the pipe has an outer surface temperature of 65°c and an emissivity of 0.85. if the rate of heat loss from the pipe surface is 0.95 kw per meter of length, the external convective heat transfer coefficient (h) is: (a) 12.5 w/m"k (b) 18.6 w/mk (c) 23.7 w/mk (d) 27.9 w/mk (e) 33.5 w/mk

Which of the following components of a pid controlled accumulates the error over time and responds to system error after the error has been accumulated? a)- proportional b)- derivative c)- integral d)- on/off.

An engine runs on the ideal diesel cycle. the cycle has a compression ratio of 20 and a cutoff ratio of 2. the highest temperature in the cycle is 1200 k. if the heat into the system is 300 kj/kg of working fluid and using variable specific heats determine the work produced per mass of working fluid