Question #3769

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?

Expert's answer

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 c^{2},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 c^{2} 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.

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 c

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 c

= 18.5 + 229320 / 5625000000 =

= 18.5 + 0.000040768 =

= 18.500040768 C.

Answer: T0 = 18.500040768 C.

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