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Heat and Thermodynamics question

2013 · Q156
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Heat and Thermodynamics question

2013 · Q156

NEETPhysicsHeat and ThermodynamicsMCQ+4 / −1
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of CpCp{{{C_p}} \over {{C_p}}}Cp​Cp​​ for the gas is
  1. A
    53{5 \over 3}35​
  2. B
    32{3 \over 2}23​
  3. C
    43{4 \over 3}34​
  4. D
    2
View written solutionFree

Correct answer: B

According to question P∝T3P \propto {T^3}P∝T3

But as we know for an adiabatic process the pressure P∝Tγγ−1P \propto {T^{{\gamma \over {\gamma - 1}}}}P∝Tγ−1γ​

So, γγ−1=3⇒γ=32{\gamma \over {\gamma - 1}} = 3 \Rightarrow \gamma = {3 \over 2}γ−1γ​=3⇒γ=23​

∴\therefore∴ CpCv=32 {{{C_p}} \over {{C_v}}} = {3 \over 2}Cv​Cp​​=23​

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