Question

One mole of an ideal gas is enclosed in a cylinder fitted with a frictionless piston and occupies a volume of 1.5 litre at a pressure of 1.2 atm. It is subjected to a process given by equation T=αV2,γ (adiabatic constant) for the gas =1.5. Choose the wrong statement. Given Rα=80 J mol−1lit−2(R= gas constant and α is constant)

The P−V diagram of the process is a straight line.

Answer 1

The statement regarding the P-V diagram of the gas being a straight line in the process described by the equation T=αV^2 is incorrect; for an ideal gas undergoing an adiabatic process, the P-V diagram would show a curve reflecting the adiabatic relationship PV^γ = constant.

Step-by-step explanation:

The question pertains to the process of an ideal gas undergoing a transformation governed by a specific relationship between temperature ("T") and volume ("V") given by the equation "T=αV^2", in a cylinder with a frictionless piston. In such a case, the pressure-volume ("P-V") diagram does not represent a straight line but a curved one that reflects the change in both pressure and volume during the adiabatic process. For adiabatic processes, the product of pressure and volume raised to the power of the adiabatic index (gamma, γ) is a constant ("PV^γ = constant"). Here, gamma is given as 1.5 and is the ratio of the specific heats ("Cp/Cv").

Additionally, the provided equations and constants, such as the ideal gas constant ("R") and the constant alpha ("α"), assist in describing the behavior of the ideal gas under the specified conditions. The given relationship involving "Rα" further emphasizes how temperature and volume are interdependent in the context of the ideal gas law, "PV = nRT".