Physics-
General
Easy

Question

22 g of carbon dioxide at 27℃ is mixed in a closed container with 16 g of oxygen at 37℃. If both gases are considered as ideal gases, then the temperature of the mixture is

  1. 24.2℃    
  2. 28.5℃    
  3. 31.5℃    
  4. 33.5℃    

The correct answer is: 31.5℃


    For carbon dioxide, number of moles open parentheses n subscript 1 end subscript close parentheses equals fraction numerator 22 over denominator 44 end fraction equals fraction numerator 1 over denominator 2 end fraction blank semicolon
    molar specific heat of C O subscript 2 end subscript at constant volume C subscript V end subscript subscript 1 end subscript equals 3 blank R
    For oxygen, number of moles open parentheses n subscript 2 end subscript close parentheses equals fraction numerator 16 over denominator 32 end fraction equals fraction numerator 1 over denominator 2 end fraction semicolon
    molar specific heat of O subscript 2 end subscript at constant volume C subscript V end subscript subscript 2 end subscript equals fraction numerator 5 R over denominator 2 end fraction.
    Let T K be the temperature of mixture.
    Heat lost by O subscript 2 end subscript = Heat gained by C O subscript 2 end subscript.
    n subscript 2 end subscript C subscript V end subscript subscript 2 end subscript increment T subscript 2 end subscript equals n subscript 1 end subscript C subscript V end subscript subscript 1 end subscript increment T subscript 1 end subscript
    fraction numerator 1 over denominator 2 end fraction open parentheses fraction numerator 5 over denominator 2 end fraction R close parentheses open parentheses 310 minus T close parentheses equals fraction numerator 1 over denominator 2 end fraction cross times open parentheses 3 R close parentheses open parentheses T minus 300 close parentheses
    Or 1550negative 5 T equals 6 T minus 1800
    Or T equals 304.54 K equals 31.5 ℃

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