# Does temperature change if change in internal energy is zero?

Find $$ΔU$$ for the combustion of methane in a sealed rigid adiabatic container.

Solution says since $$q = 0$$ and $$w = 0,$$ so $$ΔU = 0$$ by the first law of thermodynamics.

Why isn't the heat released during combustion considered?

Does the temperature of the system changes during the process? I know that

$$ΔU = nC_VΔT$$

is not valid directly as the amount of substance is changing, and so do the degrees of freedom.

• The answer to you first doubt is that the temperature of the products is higher than the temperature of the reactants in adiabatic combustion. That's where the "heat" goes. Your 2nd doubt answers itself. Feb 27, 2021 at 13:05
• Sir if temperature is increasing , the way I am calculating ΔU is by ( Uₚ - Uᵣ ) but after writing the expression with help of U = fnRT/2 (Where f = degree of freedoms) , I am not getting ΔU = 0 , please tell where I am going wrong whether this method of calculating ΔU is wrong or something else ? Feb 27, 2021 at 16:44
• Do you know how to determine $\Delta U$ if the final temperature were equal to the initial temperature (taking into account that there have been changes in the amounts of chemical species present)? Would you know $\Delta H$ for the case where the initial and final temperatures are equal? Feb 27, 2021 at 17:01
• I guess ΔH could be written with help of bond enthalpy , and ΔU is where I am confused ,according to my previous logics ΔU should come out to be zero. Feb 27, 2021 at 17:26
• $\Delta H$ is the heat of combustion which you look up or calculate from tabulated heats of formation. Do you know how to do that? If you don't know how to use this to determine $\Delta U$ at constant temperature for the reaction, you need to research that. This is in every thermo book. Once you have that, you need to determine what the temperature rise of the products would have to be in order for the overall $\Delta U$ to be zero. Feb 27, 2021 at 19:38