Since greater mass is used every time, the normal force on cup i.e. N increases which in turn increases the frictional force. So since GPE is fixed, work done by friction is also fixed but it requires small d (distance) to dissipate the same amount of GPE.
I ran into a confusion here. With the given values of diameter, emissivity and temperature for the floor how could it emit or absorb radiation at a rate of 660 W if it is in equilibrium with the dome? Because using the Stefan-Boltzmann law, I calculated a much higher value of emission or...
I guess $$I'$$ is your moment of inertia, not the angular momentum as you are saying. There is a also a little ambiguity about the axis wrt to which $$I'$$ is calculated.
You can imagine a box shaped structure whose height is that of the difference between the given altitudes and the upper and lower surfaces have area A. Then calculate the total electric flux through the box. Assume a charge density $$\rho$$ and calculate total charge inside the box. Then...
Firstly you can not use the relation $$\Delta S= \Delta Q/T$$ to find out entropy change for water, because here T is changing. Instead you should use the general relation $$\Delta S= \int dQ/T$$ to find out the change in entropy. This process should work out.