There is an iron plate with an area of $2[$m$^2]$ facing the hot side. The surface temperature of the hot side is $1,250[]$ and the temperature of the iron plate is $500[].$ What is the amount of heat generated by radiation? $($However$,$ the effective radiation constant of hot objects and iron plates is $4\mathrm{.}3\backslash$times $10".$

In a heater made of copper, $500[$kg$)$ of oil is heated with steam from $60[]$ to $200[].$ The temperature of water vapor is $240[],$ the overall heat transfer coefficient is $500[$kcal$/$m$^2$hr$.],$ and the specific heat of oil is $10[$kcal$/$kg$].$

$(1)$ What is the logarithmic average temperature difference $[]?$

$(2)$ How many $[$m$^2]$ is the

heating area?

There is a water vapor pipe $($outer diameter $100$ mm$)$ for warming in a room at $24[],$ and its surface temperature is $40[].$ The emissivity is $0\mathrm{.}92.$ How much $[$kcal$/$hr$]$ is the heat loss radiated per $1[$m$]$ of pipe length?