Worksheet 2 CHEM 401 Instructor: Dr. Afra Panahi 1. Calculate the work involved when one mole of a perfect gas is compressed under constant external pressure (5 bar) from 25 dm3 to 5 dm3 at temperature of 300K. 𝑊 = − ∫ 𝑃𝑒𝑥𝑡 𝑑𝑉 𝑊 = −𝑃𝑒𝑥𝑡 ∆𝑉 𝑊 = −𝑃𝑒𝑥𝑡 (𝑉2 − 𝑉1 ) 𝑊 = −5(5 − 25) 𝑊 = 100 𝑑𝑚3 𝑏𝑎𝑟 ∙ 105 𝑃𝑎 0.13 𝑚3 1 𝑘𝐽 ∙ ∙ 𝑏𝑎𝑟 𝑑𝑚3 1000 𝐽 𝑾 = 𝟏𝟎 𝒌𝑱 2. Calculate the work involved when one mole of a perfect gas is compressed reversibly from 25 dm3 to 5 dm3 at constant temperature of 300K. Compare your results with problem 1. 𝑊 = − ∫ 𝑃𝑑𝑉 𝑉2 𝑊 = −𝑛𝑅𝑇 𝑙𝑛 ( ) 𝑉1 5 1 𝑘𝐽 𝑊 = −(1)(8.314)(300)𝑙𝑛 ( ) = 4014.26 𝐽 ∙ 25 1000 𝐽 𝑾 = 𝟒. 𝟎𝟏 𝒌𝑱 3. (a) Calculate the maximum amount of work involved in expanding 5.00 moles of a perfect gas isothermally at 300.00K from 40.00 dm3 to 100.00 dm3. 𝑊𝑀𝐴𝑋 = − ∫ 𝑃𝑑𝑉 𝑉2 𝑊𝑀𝐴𝑋 = −𝑛𝑅𝑇 𝑙𝑛 ( ) 𝑉1 𝑊𝑀𝐴𝑋 = −(5)(8.314)(300) 𝑙𝑛 ( 𝑊𝑀𝐴𝑋 = −11427.06 𝐽 ∙ 1 𝑘𝐽 1000 𝐽 100 ) 40 𝑾𝑴𝑨𝑿 = −𝟏𝟏. 𝟒𝟑 𝒌𝑱 (b) Calculate the minimum amount of work required to compress 5.00 moles of a perfect gas isothermally at 300K from 100 dm3 to 40.0 dm3. 𝑊𝑀𝐼𝑁 = − ∫ 𝑃𝑑𝑉 𝑉2 𝑊𝑀𝐼𝑁 = −𝑛? ...
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