Question

An ordinary egg can be approximated as a 5.5-cm diameter sphere. The egg is initially at a uniform temperature of 8°C and is dropped into boiling water at 97°C. Taking the properties of the egg to be r 1020 kg/m3 and cp 3.32kJ/kg · °C, determine (a) how much heat is transferred to the egg by the time the average temperature of the egg rises to70°C and (b) the amount of entropy generation associated with this heat transfer process.

Answer 1

a)
`Q_(in) = 13.742\,kW`, b)
`\Delta S = 370.15\,(kJ)/(K)`

Step-by-step explanation:

a) The heat transfered to the egg is computed by the First Law of Thermodynamics:

`Q_(in) +U_(sys,1) - U_(sys,2) = 0`

`Q_(in) = U_(sys,2) - U_(sys,1)`

`Q_(in) = \rho_(egg)\cdot \left((4\pi)/(3)\cdot r^(3)\right)\cdot c \cdot (T_(2)-T_(1))`

`Q_(in) = \left(1020\,(kg)/(m^(3))\right)\cdot \left((4\pi)/(3)\right)\cdot (0.025\,m)^(3)\cdot \left(3.32\,(kJ)/(kg\cdot ^(\textdegree)C) \right)\cdot (70\,^(\textdegree)C - 8\,^(\textdegree)C)`

`Q_(in) = 13.742\,kW`

b) The amount of entropy generation is determined by the Second Law of Thermodynamics:

`\Delta S = (Q_(in))/(T_(in))`

`\Delta S = (13.742\,kJ)/(370.15\,K)`

`\Delta S = 370.15\,(kJ)/(K)`