Answer to Question #3769 in Electric Circuits for giroux

Question

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?

Answer 1

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.

Answer: T0 = 18.500040768 C.