During an adiabatic process, pressure of gas is found to be proportional to the cube of its temperature. The ratio of Cp/Cv is
Correct answer: A. 1.5
- A. 1.5
- B. 44319
- C. 44257
- D. 44289
Explanation
Answer: 1.5Given that, p∝T³ or pT^-3 = constant .....(i) Also for adiabatic process pV^Γ = constant but pV=RT (ideal gas law) or V= RT/p =p(RT/p)^Γ= constant (p^1−Γ) (T^Γ)= constant or pT^Γ /(1−Γ) = constant Equating Eqs. (i) and (ii), we get Γ/1−Γ =−3 orΓ=−3+3Γ or 2Γ=3 =Γ=3/2 Cp/Cv =3/2 Cp/Cv = 1.5
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About Molar Specific Heat of a Gas
Molar specific heat is the heat required to raise the temperature of one mole of a gas by one kelvin, expressed through Q = nCΔT. Questions compare the constant volume value Cv with the constant pressure value Cp, apply the ideal gas relation Cp − Cv = R, and identify how the thermodynamic process affects heat capacity.
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