One mole of an ideal gas (Cp = 7/2R and Cv = 5/2R) undergoes a two-step process: (1) From T = 800 [K] and P = 4[bar] the gas is cooled at constant pressure to T = 300[K]. (2) The gas is then heated at constant volume until its temperature reaches 800 [K]. If this two-step process is replaced by a single isothermal expansion of the gas from 800 [K] and 4 [bar] to some final pressure P, what is the value of P that makes the work of the two processes the same?

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One mole of an ideal gas (Cp = 7/2R and Cv = 5/2R) undergoes a two-step process:

(1) From T = 800 [K] and P = 4[bar] the gas is cooled at constant pressure to T = 300[K].
(2) The gas is then heated at constant volume until its temperature reaches 800 [K].

If this two-step process is replaced by a single isothermal expansion of the gas from 800 [K] and 4 [bar] to some final pressure P, what is the value of P that makes the work of the two processes the same?

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