A piece of charcoal and a piece of shining steel of the same area are kept for a long time in an open lawn in bright sun.
a) The steel will absorb more heat than the charcoal
b) The temperature of the steel will be higher than that of the charcoal
c) If both are picked up by bare hands, the steel will be felt hotter than the charcoal
d) If the two are picked up from the lawn and kept in a cold chamber, the charcoal will lose heat at a faster rate than steel

Initially both steel and charcoal have same temperature. Finally also they will have same temperature (temperature of surrounding).

For simplicity, assuming both to be in the form of spheres having same surface area. It means their radius is same. Now, $Q=mc∆\theta =\left(\frac{4}{3}{\mathrm{\pi R}}^3\mathrm{\rho }\right)c∆\theta \propto c\rho$. Now product $c\rho$ for steel is roughly $\left(490\times 8000\right)$ which is much greater than that for charcoal $\left(840\times 400\right)$. Hence steel will absorb more heat than charcoal.

After keeping them for a long time in air, both (steel and charcoal) will have temperature of the surrounding. Thermal conductivity of steel is greater than that of charcoal. So when they are touched with bare hands, rate of heat conducted by steel to our body is more than that by charcoal. This makes us feel steel is hotter (even though both have same temperature).

By Stefan's law, rate of loss of heat from a body, $\sigma \epsilon A{T}^4\propto \epsilon$. Charcoal is more closer to a black body than steel is. Emissivity of charcoal is greater than that of steel. Hence, when both (at same temperature) are kept inside cold chamber, the charcoal will lose heat at a faster rate than steel.