Chemistry, asked by mdmadhudixit, 1 year ago

When an ideal gas with pressure P and volume V is compressed isothermally to one fourth of its volume, the pressure is P1. When the same gas is compressed polytropically according to the equation PV1.5 = constant to one fourth of its initial volume, the pressure is P2. The ratio of (P1/P2) is

Answers

Answered by KaurSukhvir
0

Answer:

The ratio of (P₁/P₂)  is equal to 1/2.

Explanation:

For Isothermal process, PV=constant

                            PV=P_{1}( \frac{V}{4} )

                            P_{1} =4P                          ...................(1)

For polytropically process,  PV^{1.5} =constant

                            PV^{1.5} =P_{2}( \frac{V}{4})^{1.5}

                            P_{2}=8P                        ....................(2)

By dividing eq. (1) by eq.(2)

                             \frac{P_{1} }{P_{2} } =\frac{1}{2}

Therefore,  the ratio of  \frac{P_{1} }{P_{2} } is equal to  \frac{1}{2}.

Answered by syed2020ashaels
0

Answer:

The ratio of (P₁/P₂)  is equal to \frac{1}{2}.

Explanation:

  • For Isothermal process, we know that temperature remains constant
    PV = nRT
  • Now as we know n and R are number of moles and Rydberg's constant hence
    PV = Constant
    P_{1}V_{1} = P_{2}V_{2}\\
  • Now according to question we assume
    P_{1} = P ,  V_{1} = V then P_{2} = P' and V_{2} = \frac{V}{4}
  • Now when we put the values in the above equation we get
    P' = 4P  ....................(1)
  • For polytropically process, we know PV^Y = Constant
    P_{1}V_{1}^Y = P_{2}V_{2}^Y
    So P_{1}V_{1}^1^.^5 = P_{2}V_{2}^1^.^5 = Constant
  • Now according to question we assume
    P_{1} = P , V_{1} = V then P_{2} = P' and V_{2} = \frac{V}{4}
  • By putting these values in the equation we get
    P' = 8P  ....................(2)
  • By dividing eq. (1) by eq.(2) we get
    \frac{P_{1}}{P_{2}}  = \frac{1}{2}

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