A lagged stick of cross-section area $1 {\mathrm{cm}}^2$ length are $1 {\mathrm{cm}}^2$ and length $1 \mathrm{m}$ is initially at a temperature of $0^{°}\mathrm{C}$. It is then kept between $2$ resevoirs of temperature ${100}^{°}\mathrm{C}$ and $0^{°}\mathrm{C}.$ Specific heat capacity is $10 \mathrm{J} {\mathrm{kg}}^{°}\mathrm{C}$ and linear mass density is $2 \mathrm{kg} {\mathrm{m}}^{-1}$.

(i) If temperature gradient along the rod in steady state is $-50 \mathrm{n} °\mathrm{C} {\mathrm{m}}^{-1}$ then find the value of $n$. 

(ii) If total heat absorbed by the rod to reach steady state is $250 \mathrm{n} \mathrm{J}$ then find the value of $n$.