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:

A

$$\dfrac{\alpha E_0}{m\,s}\left(1-e^{-\lambda t}\right)$$

B

$$\dfrac{\alpha E_0}{m\,s}\left(e^{\lambda t}-1\right)$$

C

$$\dfrac{\lambda E_0}{m\,s}\left(1-e^{-\lambda t}\right)$$

D

$$\dfrac{E_0}{m\,s}\left(\alpha-\lambda e^{-\lambda t}\right)$$