Consider two containers A and B containing identical gases at the same pressure, volume and temperature. The gas in container A is compressed to half of its original volume isothermally while the gas in container B is compressed to half of its original value adiabatically. The ratio of final pressure of gas in B to that of gas in A is

(a) $2^{\mathit{\gamma }-1}$  

(b) ${\left(\frac{1}{2}\right)}^{\mathit{\gamma }-1}$   

(c) $({\frac{1}{1-\mathit{\gamma }})\mathit{}\mathit{}}^2$  

(d) ${\left(\frac{1}{\mathit{\gamma }-1}\right)}^2$  

This is a multiple choice answer as classified in NCERT Exemplar

(a) Container A is isothermal and container B is adiabatic

For isothermal process P₁V₁=P₂V₂

P_o (2V_o)= P₂ (V_o)

P₂= 2P_o

for adiabatic process

P₁V₁^y= P₂V₂^y

P_o (2V_o)^y=P₂ (V_o)^y

P₂= ( $\frac{2V_o}{V_o}$ )^yP_o= 2^yP_o

Hence ratio of final pressure = $\frac{2^{\gamma }{P}_o}{2P_o}=2^{\gamma -1}$

<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (a) Container A is isothermal and container B is adiabatic</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745477511phpM0sUL3_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745477511phpM0sUL3.jpeg" alt="" width="305" height="176"></picture></div></div><p>For isothermal process P₁V₁=P₂V₂</p><p>P_o (2V_o)= P₂ (V_o)</p><p>P₂= 2P_o</p><p>for adiabatic process</p><p>P₁V₁^y= P₂V₂^y</p><p>P_o (2V_o)^y=P₂ (V_o)^y</p><p>P₂= (<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>2</mn> <msub> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </math> </span>)^yP_o= 2^yP_o</p><p>Hence ratio of final pressure = <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msup> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow> <mrow> <mi>γ</mi> </mrow> </mrow> </msup> <msub> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <msub> <mrow> <mrow> <mi>P</mi> </mrow> </mrow> <mrow> <mrow> <mi>o</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mi> </mi> <msup> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow> <mrow> <mi>γ</mi> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> </math> </span></p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment