A metal ball of diameter $$60mm$$ is initially at $${220^ \circ }C.$$ The ball is suddenly cooled by an air jet of $${20^ \circ }C.$$ The heat transfer coefficient is $$200\,W/{m^2}.K.$$ The specific heat, thermal conductivity and density of the metal ball are $$400\,\,J/kg.K,\,\,400\,\,W/m.K$$ and $$\,9000\,\,kg/{m^3},$$ respectively. The ball temperature (in $${}^ \circ C$$) after $$90$$ seconds will be approximately.

The emissive power of a blackbody is $$P.$$ If its absolute temperature is doubled, the emissive power becomes

In a counter-flow heat exchanger, water is heated at the rate of $$1.5kg/s$$ from $$\,40{}^ \circ C\,$$ to $$\,80{}^ \circ C\,$$ by an oil entering at $$\,120{}^ \circ C\,$$ and leaving at $$\,60{}^ \circ C\,$$. The specific heats of water and oil are $$4.2kJ/kgK$$ and $$2kJ/kgK,$$ respectively. The overall heat transfer coefficient is $$400\,W/{m^2}K.$$ The required heat transfer surface are (in $${m^2}$$) is

The standard deviation of linear dimensions $$P$$ and $$Q$$ are $$3\mu m$$ and $$4\mu m$$, respectively. When assembled, the standard deviation (in $$\mu m$$) of the following linear dimension $$(P+Q)$$ is ___________.