If the heater is made out of pure solid Aluminum (its density is 2702kg/m3 and i
ID: 2238656 • Letter: I
Question
If the heater is made out of pure solid Aluminum (its density is 2702kg/m3 and its specific heat is 903J/kg/K) and if it was initially at room temperature (300K) determine how long it takes for the heater to reach 95% of its steady temperature value which we calculated it to be 72.4oC. (Hints: The process is not steady state; the system (i.e. the heater) is a solid, hence incompressible. Start with the rate form of the 1st Law of thermodynamics to produce a differential equation with temperature and time being the variables.)Explanation / Answer
E'input - E'output = E'internal {first law} Q' - k*(T - 300) = (rho)*volume*(specific heat)*(dT/dt) dT/dt = 0 at at T = 72.4 273 = 345.4K Q' - k*(345.4 - 300) = k = 0.022*Q' so the equation now becomes Q'*[1 - 0.022*(T - 300)] = (rho)*volume*(specific heat)*(dT/dt) now substituting values of Q', density (rho), volume and specific heat and then integrating we get the Temperature as a function of time.