A volume of air assumed to be an ideal gas is first cooled without changing its

Question

A volume of air assumed to be an ideal gas is first cooled without changing its volume and Then expended without changing its pressure. As shown here, take the graduation p_0= 2.5x10^5 pa and the graduation v_0= 0.05. How does the final temperature of the gas compare with its initial temperature? How much heat does the air exchange with its during the process abc? (in jouls, 2sig) Do the air absorb heat or release heat? If the air instead expends from state a to state c by the straight-line path shown, hour much heat does it exchange with its surrounding. (in , )

Explanation / Answer

  I suppose we're to assume that p is first reduced by a factor of 3, and that V is then expanded by a factor of 3.

A). The final temperature is the same as the initial temperature, since the final product pV is the same as the initial pV. Two significant digits? Only if my assumption about the factors of 3 are correct to 2 significant digits.

B). The change in internal energy was zero, since the temperature change was zero. The work done by the air was
p delta-V for the "bc" process and zero for the "ab" process.
(50000 Pa)(0.02 m^3) = 1000 J. This is equal to the net heat absorbed by the gas in the abc process. 1000 J.

D) The geometry indicates that W would be twice as great for the "ac" process, and the delta-U would still be zero, so the heat absorbed by air would be 2000 J.

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