To solve this problem we need to consider the specific heat of water and glass. We then need to right an equation for the total heat transfer in the system, which should be zero.

This problem involves the latent heat of vaporization of water and the first law of thermodynamics for an isobaric process

To find $\Delta V$ you will need to consider the steam as an ideal gas, as we did when deriving the molar specific heat of an ideal gas at constant pressure.

As we saw from the equipartition theorem an ideal diatomic gas should have a constant volume molar heat capacity of $c_{V,m}=\frac{5}{2}R$. Is this process constant volume or constant pressure?

Once you have decided on the appropriate molar heat capacity you will need to determine the number moles of gas. You can do this using the ideal gas law $PV=nRT$.

You will need to use the result we obtained that for the quasistatic adiabatic expansion of an ideal gas that $PV^{\gamma}=\mathrm{constant}$ and that for any ideal gas $PV=nRT$.

A radiative heat transfer problem. To work out the temperature change approximate that all the heat is coming from the water.

A heat conduction problem. I only realized after posting that it uses British thermal units and R values..which we did not talk about in class! Information about these things is in your textbook.