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AP EAMCET · PHYSICS · Kinetic Theory of Gases

A gas of mass ' \(\mathrm{m}\) ' and molecular weight ' \(\mathrm{M}\) ' is flowing in an insulated tube with a velocity ' \(2 \mathrm{~V}\) '. If the flow of the gas is suddenly stopped and all the kinetic energy is utilized to compress the gas, the increases in the temperature of the gas is ( \(\gamma\) is ratio of specific heats, \(\mathrm{R}\) is universal gas constant)

  1. A \(\frac{2 \mathrm{MV}^2(\gamma-1)}{\mathrm{R}}\)
  2. B \(\frac{\mathrm{mV}^2(\gamma-1)}{2 \mathrm{MR}}\)
  3. C \(\frac{\mathrm{mV}^2 \gamma}{2 \mathrm{R}}\)
  4. D \(\frac{\mathrm{MV}^2 \gamma}{2 \mathrm{R}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{2 \mathrm{MV}^2(\gamma-1)}{\mathrm{R}}\)

Step-by-step Solution

Detailed explanation

Since the gas flow is suddenly stopped. We will Consider it to be an adiabatic process. Work done in a adiabatic process \[ \mathrm{W}=\frac{\mathrm{nR} \Delta \mathrm{T}}{\gamma-1}=\frac{\mathrm{mR} \Delta \mathrm{T}}{\mathrm{M}(\gamma-1)} \] Energy available after the gas flow…