Tutor profile: Saikat C.

Draw the relation between the COP of a refrigerator and a heat engine

Let the engine draw energy Q1 from the cold region and throw Q2 to warmer region, while work being 'W' done on it. COP= Desired Effect/ Work Done For Heat Engine Desired effect is Q2 and for refrigerator is Q1 Thus COP| refrigerator= Q1/W COP| heat engine= Q2/W But Q1+W=Q2 Therefore, COP| heat engine= (Q1+W)/W=1+Q1/W=1+COP|refrigerator.

Air is passed through a convergent-divergent nozzle. It is seen that by decreasing the throat dia the velocity increases. What can be inferred about the flow?

Sub-sonic flow, i.e Mach no.<1 At Mach no.=1 flow becomes 'choked', i.e mass flow rate is maximum.

For the quadratic function f(x)=x^2+K.x+4, find the range of 'k' such that the minimum value of the function is greater than '0'

Minimum/ maximum value of a function is when df(x)/dx=0 => 2x+k=0 => x=-k/2 [It is minimum because d2f(x)/dx2>0 always] Thus min(f(x))=k^2/4-k^2/2+4>0 =>k^2/4<4 => k^2<16 => k:[-4,4]