Find the error in the following proof that 2 = 1. consider equation = multiply both sides of to obtain 2 = substract 2 from both sides to get 2 − 2 = − 2 . now factor each side, + − = − and divide each side by − to get + = finally, let and equal to 1, which shows that 2 = 1

Apiston-cylinder with a volume of 0.25 m3 holds 1 kg of air (r 0.287 k/kgk) at a temperature of 100 c. heat transfer to the cylinder causes an isothermal expansion of the piston until the volume triples. how much heat is added to the piston-cylinder?

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.

What is the correct way to measure the overall length of a boat? measure from the tip of the bow to the highest point on the gunwale. measure from the tip of the bow in a straight line to the stern of the boat. measure from the tip of the bow in a straight line to the back seat. measure from port to starboard at the boat's widest point.