Tru Physics

Problem 1.50 (Schroeder’s Intro to Thermal Physics)

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Problem 1.50

Consider the combustion of one mole of methane gas:

CH_4(gas) + 2O_2(gas) \rightarrow CO_2(gas) + 2H_2O(gas).

The system is at standard temperature (298 K) and pressure (10^5 Pa) both before and after the reaction.

(a) First imagine the process of converting a mole of methane into its elemental consituents (graphite and hydrogen gas). Use the data at the back of this book to find \Delta H for this process.
(b) Now imagine forming a mole of CO_2 and two moles of water vapor from their elemental constituents. Determine \Delta H for this process.

(c) What is \Delta H for the actual reaction in which methane and oxygen form carbon dioxide and water vapor directly? Explain.
(d) How much heat is given off during this reaction, assuming that no “other”
forms of work are done?
(e) What is the change in the system’s energy during this reaction? How would
your answer difer if the H_2O ended up as liquid water instead of vapor?

(f) The sun has a mass of 2 \cdot 10^{30}kg and gives off energy at a rate of 3.9 \cdot 10^{26}watts. If the source of the sun’s energy were ordinary combustion of a chemical fuel such as methane, about how long could it last?

Solution:

Problem 1.50

Find more Schroeder solutions here.

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