Let$$s think about the thermodynamics involved in driving your car. In your car engine, chemical energy of gasoline is converted to work by combustion followed by expansion$/$compression of a piston. Consider a simple model of this process.

a$)1$ mole of an ideal gas initially at $300$K and $1$ atm is heated and allowed to expand reversibly at constant pressure against a piston until the final temperature is $600$K$.$ The constant pressure heat capacity of this gas is CP$,$m $=3\mathrm{.}5$R$.$ Compute the enthalpy change $$H for this process, and compare to the values of $$U$,$ q$,$ w that you computed in problem $3$ of Problem Set $2.$ Comment on your results.

b$)$ In your car, this required energy comes from conversion of chemical bonds $($chemi$-$ cal reaction$).$ For simplicity, consider converting methane $($CH$4)$ and oxygen $($O$2)$ to water $($vapor$)$ and carbon dioxide. Write a balanced chemical reaction and use the enthalpies of formation found in Table A$\mathrm{.}5-7$ in Tinoco, to calculate the heat released from burning one mole of methane.

c$)$ comment on the difference in magnitude of the enthalpies computed in parts a$)$ and b$).$ Assume that the gas tank in your car holds the equivalent of $1200$ moles of methane, how much heat can be produced by burning the entire tank of gas?

Attached Problem set $2$ question $3.$