A heat-conducting piston divides a closed, thermally insulated cylinder of ideal gas ( γ ) into two equal parts at T 0 . The piston is slowly displaced until the ratio of the larger to smaller volum

Question

A heat-conducting piston divides a closed, thermally insulated cylinder of ideal gas ( γ ) into two equal parts at T 0 ​ . The piston is slowly displaced until the ratio of the larger to smaller volume is η . The gas temperature is:

TestHub · Accepted Answer

Both parts share one temperature T and the process is reversible and insulated, so T ( γ − 1 ) 2 ​ V 1 ​ V 2 ​ = constant . With V 1 ​ V 2 ​ = ( η + 1 ) 2 η V 2 ​ against 4 V 2 ​ initially, ( T 0 ​ T ​ ) ( γ − 1 ) 2 ​ = 4 η ( η + 1 ) 2 ​ .

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