Activity (Decay Rate)

A nuclear reactor starts producing a radioactive nuclide $$X$$ from $$t=0$$, at a constant rate of $$\alpha$$ per second. Each decay of $$X$$ produces energy $$E_0$$, which is utilized to heat a liquid of mass $$m$$ and specific heat $$s$$. Assuming no heat loss from the liquid and taking $$\lambda$$ as the decay constant of $$X$$, the rate of increase in the temperature of the liquid is: