Nuclei · Question 1

A nuclear reactor starts producing a radioactive nuclide X from t=0, at a constant rate of per second. Each decay of X produces energy E0, which is utilized to heat a liquid of mass m and specific heat s. Assuming no heat loss from the liquid and taking as the decay constant of X, the rate of increase in the temperature of the liquid is:

1. E0m s (1-e- t )
2. E0m s (e t-1 )
3. E0m s (1-e- t )
4. E0m s ( - e- t )

Answer

(1) E0m s (1-e- t )

Solution

Key idea: dNdt= - N with N(0)=0.

Solving: N= (1-e- t ), so activity N= (1-e- t ).

Power delivered to liquid = N E0=m s dTdt.

dTdt= E0m s (1-e- t ).

Answer: (A)