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JEE Main 2013 (22 Apr, Shift 1) · Thermodynamic Processes

Thermodynamic Processes question from JEE Main 2013 (22 Apr, Shift 1)

Q237JEE Main 2013 · 22 APR · SHIFT 1Medium

Thermodynamic Processes

An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes 32 times of its initial value. If the final pressure of gas is 128 atmospheres, the value of 'γ\gamma' of the gas is:

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Answer: (b)

  1. ρ∝1V\rho \propto \frac{1}{V}, so adiabatic gives P∝ργP \propto \rho^{\gamma}.
  2. 1281=32γ⇒27=25γ\frac{128}{1} = 32^{\gamma} \Rightarrow 2^7 = 2^{5\gamma}
  3. γ=75=1.4\gamma = \frac{7}{5} = 1.4
  4. So the answer is (b) 1.4.
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