An insulated container containing monoatomic gas of molar mass m is moving with a velocity Vo . If the container is suddenly stopped, find the change in temperature.

<p><span data-teams="true">This is a short answer type question as classified in NCERT Exemplar</span></p><p>According to kinetic interpretation of temperature, absolute temperature of a given sample of a gas is proportional to total translational kinetic energy of its molecule.</p><p>Hence any change in absolute temperature of a gas will contribute to corresponding change in translational KE and vice versa.</p><p>N= number of moles</p><p>m=molar mass of the gas</p><p>when the container stops its total kinetic energy transferred to the gas molecules in the form of translational KE, thereby increasing the absolute temperature.</p><p>KE of molecules due to velocity KE=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mo> (</mo> <mi>m</mi> <mi>n</mi> <mo>)</mo> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> </math> </span></p><p>Increase in translational KE =n<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi>R</mi> <mo>? </mo> </math> </span>T</p><p>According to kinetic theory&nbsp; of gases</p><p><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mo> (</mo> <mi>m</mi> <mi>n</mi> <mo>)</mo> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> </math> </span>= n<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi>R</mi> <mo>? </mo> </math> </span>T</p><p><span contenteditable="false"> <math> <mo>? </mo> </math> </span>T=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>m</mi> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> <mi>R</mi> </mrow> </mrow> </mfrac> </math> </span></p>

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