Thermal Physics Questions

If the cold junction of a thermocouple is kept at $0{}^{\circ }\text{C}$ and the hot junction is kept at $T{}^{\circ }\text{C}$, then the relation between neutral temperature ($T_n$) and temperature of inversion ($T_i$) is:

Assuming the sun to have a spherical outer surface of radius $r$, radiating like a black body at temperature $t{}^{\circ }\text{C}$, the power received by a unit surface, (normal to the incident rays) at a distance $R$ from the centre of the sun is:

A black body is at $727{}^{\circ }\text{C}$. It emits energy at a rate that is proportional to:

An engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62{}^{\circ }\text{C}$, its efficiency is doubled. The temperature of the source is: