Physics-
General
Easy

Question

Carbon monoxide is carried around a closed cycle abc in which bc is an isothermal process as shown in the figure. The gas absorbs 7000 J of heat as its temperature increases from 300 K to 1000 K in going from a to b. The quantity of heat rejected by the gas during the process ca is

  1. 4200 J    
  2. 5000 J    
  3. 9000 J    
  4. 9800 J    

The correct answer is: 9800 J


    For path ab : left parenthesis capital delta U right parenthesis subscript a b end subscript equals 7000   J
    By using capital delta U equals mu C subscript V end subscript capital delta T
    7000 equals mu cross times fraction numerator 5 over denominator 2 end fraction R cross times 700 rightwards double arrow mu equals 0.48
    For path ca :
    left parenthesis capital delta Q right parenthesis subscript c a end subscript equals left parenthesis capital delta U right parenthesis subscript c a end subscript plus left parenthesis capital delta W right parenthesis subscript c a end subscript (i)
    because left parenthesis capital delta U right parenthesis subscript a b end subscript plus left parenthesis capital delta U right parenthesis subscript b c end subscript plus left parenthesis capital delta U right parenthesis subscript c a end subscript equals 0
    therefore 7000 plus 0 plus left parenthesis capital delta U right parenthesis subscript c a end subscript equals 0 rightwards double arrow left parenthesis capital delta U right parenthesis subscript c a end subscript equals negative 7000   J (ii)
    Also left parenthesis capital delta W right parenthesis subscript c a end subscript equals P subscript 1 end subscript left parenthesis V subscript 1 end subscript minus V subscript 2 end subscript right parenthesis equals mu R left parenthesis T subscript 1 end subscript minus T subscript 2 end subscript right parenthesis
    equals 0.48 cross times 8.31 cross times left parenthesis 300 minus 1000 right parenthesis equals negative 2792.16   J (iii)
    on solving equations (i), (ii) and (iii)
    left parenthesis capital delta Q right parenthesis subscript c a end subscript equals negative 7000 minus 2792.16 equals negative 9792.16   J equals negative 9800   J

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