Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio V d V a and the ratio V c V b is:

Question

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio V d ​ V a ​ ​ and the ratio V c ​ V b ​ ​ is:, V d ​ V a ​ ​  = V c ​ V b ​ ​, V d ​ V a ​ ​ = V c ​ V b ​ ​, V d ​ V a ​ ​ = ( V c ​ V b ​ ​ ) − 1, V d ​ V a ​ ​ = ( V c ​ V b ​ ​ ) 2

MARKS App · Accepted Answer

For adiabatic process TV γ − 1 = constant ​ T a ​ ⋅ V a γ − 1 ​ = T d ​ ⋅ V d γ − 1 ​ ( V d ​ V a ​ ​ ) γ − 1 = T a ​ T d ​ ​ T b ​ ⋅ V b γ − 1 ​ = T c ​ ⋅ V c γ − 1 ​ ( V c ​ V b ​ ​ ) γ − 1 = T b ​ T c ​ ​ V d ​ V a ​ ​ = V c ​ V b ​ ​ ( ∵ T d ​ = T c ​ T a ​ = T b ​ ​ ) ​

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