[excursatis]

What is the entropy change when 1.00 mol of ideal gas that raises reversibly from 10 °C to 50 °C at constant pressure, constant volume, assuming the heat capacity is independent from temperature?

This is all the information given. I m assuming that the formula ΔS=Cln(T2/T1) is used. However, I do not know how the heat capacities are supposed to be obtained from the given information. I do not have the enthalpy or internal energy of the process; I cannot calculate the heat capacity from pressure or volume. Please say if my reasoning is incorrect. (These aren’t the values of the original question but this is based on Atkins Chemical Principles 5th ed. Ch 8 # 5 and 6)

[mjc123]

You can't heat a gas at constant pressure and constant volume. Either P or V (or both) must change with temperature.
Or are there two separate questions here?

[excursatis]

Sorry for the confusion. Yes, they are two separate questions.

[Enthalpy]

I don't see neither what to do better than keeping a heat capacity as a parameter. At best, notice the relation between the capacities at constant P versus contant V.

If the text added "monoatomic" you could reliably predict the heat capacity, or "diatomic without vibrations", or some similar hint.