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:
