The steady, surface temperature of a lake changes from point to point and is given to you as a function T(x, y) (assume the surface of the lake is in the (x, y) plane). If you attach a thermometer to a boat and take a path across the lake surface defined by the trajectory (x(t), y(t)) = (bi(t), b2(t)), find an expression for the rate of change of the thermometer temperature in terms of the lake temperature.

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At steady state, air at 200 kpa, 325 k, and mass flow rate of 0.5 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. the inlet cross-sectional area is 6 cm2. at the duct exit, the pressure of the air is 100 kpa and the velocity is 250 m/s. neglecting potential energy effects and modeling air as an 1.008 kj/kg k, determine ideal gas with constant cp = (a) the velocity of the air at the inlet, in m/s. (b) the temperature of the air at the exit, in k. (c) the exit cross-sectional area, in cm2

Heat transfer by is the fastest mode of heat transfer that requires no intervening medium. a)-conduction b)-convection c)-radiation d)-conduction and convection