A spring with an m-kg mass and a damping constant 3 (kg/s) can be held stretched 0.5 meters beyond its natural length by a force of 1.5 newtons. If the spring is stretched 1 meters beyond its natural length and then released with zero velocity, find the mass that would produce critical damping.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.

Refrigerant-134a enters the compressor of a refrigerator as superheated vapor at 0.14 mpa and -10°c at a rate of 0.05 ka/s and leaves at 0.8 mpa and 50°c. the refrigerant is cooied in the condenser to 0.72 mpa and 26'c. it is then throttled to 0.15 mpa. sketch the t-s diagram for the system and evaluate: 6) the rate of heat removai from the refrigerated space (kw), it) the power input to the compressor (kw), ii) the isentropic efficiency of the compressor (%), and iv) the cop of the refrigerator.

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)