The energy released from 6.25E-10 kg of mass in a nuclear reaction is used to heat a 252 kg piece of aluminum initially at 18.5 Celsius. what is the final temperature of the aluminum?
Let m1 = 6.25E-10 kg be the mass in a nuclear reaction, m2 = 252 kg be the mass of aluminium, T0 = 18.5 Celsius be the initial temperature of aluminium.
Then the energy released from m1 is equal to Q = m1 c2,where c=3*10^9 m/s is the speed of light On the other hand, to heat aluminium from T0 to T1 it is necessary to spent energy W = C m2 (T1-T0), where C - is the heat capacity (or thermal capacity) of aluminium It is known that C = 910 J/(kg K)
Thus we have that m1 c^2 = C m2 (T1-T0), T1 = T0 - C m2 / m1 c2 T1 = 18.5 + 910 * 252 / (6.25E-10 * 9E18) = = 18.5 + 229320 / 5625000000 = = 18.5 + 0.000040768 = = 18.500040768 C.