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Asked by adjacentcalliber10 | 10 May, 2019, 12:00: PM
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for adiabatic process, we have     PV γ = K  ...................(1)
 
where P is pressure, V is volume, γ is ratio of specific heat of constant volume and constant pressure and K is a constant.
 
by taking logarithm on both sides of eqn.(1), we have   ln(P) + γ ln(V) = ln(K)
 
Hence  we have,    ln(P) = ln(K) - γ ln(V) ..............................(2)
 
Eqn.(2) shows the linear relationship between ln(P) and ln(V) as shown in graphs of figure given in question with negative slope.
 
Hence slope of each graph equals the ratio of specific heat of constant volume and constant pressure.
 
slope of graph-X that represent gas-1 is greater than slope of graph-Y that represent gas-2.
 
Hence ratio of specific heats of gas-1 is graeter than that of gas-2
 
γ1 > γ2   ;
 
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space space fraction numerator begin display style R end style over denominator begin display style C subscript V 1 end subscript end style end fraction space greater than space space fraction numerator begin display style R end style over denominator begin display style C subscript V 2 end subscript end style end fraction space space space semicolon space space space space space C subscript V 2 end subscript space space greater than space C subscript V 1 end subscript end style
 
 
Specific heat is directly prportional to degrees of freedom f .  Since we have CV2 > CV1 ,  then  f2 > f1
Answered by Thiyagarajan K | 12 May, 2019, 05:24: PM
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