1. The problem statement, all variables and given/known data Hi! I need some help by my phisycs homework at universty. Here is the problem: We have a steel ball, with density of 7800kg/m^3, with speficic heat capacity 460J/kgK. Temperature of the ball is 1700K. How much time does the ball need to cool down to half of it's temperature (850K), if it cools only because of the thermal radiation. Stefan-Boltzman constant is 5,67×10^-8. There is no other radiation on the ball, from the surrounding area. The ball's mass is 1kg. 2. Relevant equations 3. The attempt at a solution I suppose, that the power of radiation (P = j × A = (s.b. constant) × T^4 × A) is decreasing as the temperature drops, so i tried to set up my equaton with differentials: dQ = Pdt mc dT = A × (sb const.) × T^4 dt i integrated the equation, and got this: mcT^-4dT = A(sb const)dt -1/3 mcT^-3= A(sb const) × t integral is from Ta/2 to Ta and i shrinked the expression and expressed time from the equation t= 8mc/(Ta)^3×A×(sb. const) ; c= spec. heat capacity sb const. = stefan boltzman constante = 5,67 × 10^-8 Ta = temp. at start = 1700K the result i get is 51 secons. The solution should be 313 seconds. What am I doing wrong? Can you help me?