Physics-
General
Easy

Question

The P-V diagram of 2 gm of helium gas for a certain process A rightwards arrow B is shown in the figure. what is the heat given to the gas during the process A rightwards arrow B

  1. 4 P subscript o end subscript V subscript o end subscript    
  2. 6 P subscript o end subscript V subscript o end subscript    
  3. 4.5 P subscript o end subscript V subscript o end subscript    
  4. 2 P subscript o end subscript V subscript o end subscript    

The correct answer is: 6 P subscript o end subscript V subscript o end subscript


    Change in internal energy from A rightwards arrow B is
    capital delta U equals fraction numerator f over denominator 2 end fraction mu R capital delta T equals fraction numerator f over denominator 2 end fraction left parenthesis P subscript f end subscript V subscript f end subscript minus P subscript i end subscript V subscript i end subscript right parenthesis
    equals fraction numerator 3 over denominator 2 end fraction left parenthesis 2 P subscript 0 end subscript cross times 2 V subscript 0 end subscript minus P subscript 0 end subscript cross times V subscript 0 end subscript right parenthesis equals fraction numerator 9 over denominator 2 end fraction P subscript 0 end subscript V subscript 0 end subscript
    Work done in process A rightwards arrow B is equal to the Area covered by the graph with volume axis i.e.,
    W subscript A rightwards arrow B end subscript equals fraction numerator 1 over denominator 2 end fraction left parenthesis P subscript 0 end subscript plus 2 P subscript 0 end subscript right parenthesis cross times left parenthesis 2 V subscript 0 end subscript minus V subscript 0 end subscript right parenthesis equals fraction numerator 3 over denominator 2 end fraction P subscript 0 end subscript V subscript 0 end subscript
    Hence, capital delta Q equals capital delta U plus capital delta W equals fraction numerator 9 over denominator 2 end fraction P subscript 0 end subscript V subscript 0 end subscript plus fraction numerator 3 over denominator 2 end fraction P subscript 0 end subscript V subscript 0 end subscript equals 6 P subscript 0 end subscript V subscript 0 end subscript

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