$(a)\;\large\frac{15}{16 ln 2}\qquad(b)\;\large\frac{16}{15 ln 2}\qquad(c)\;\large\frac{15}{16 }\qquad(d)\;\large\frac{16}{15}$

Thermodynamics

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Answer : $\;\large\frac{15}{16 ln 2}$

Explanation :

Heat absrobed during the process $\;AB=n C_{p} \bigtriangleup T\quad$ (p is constant during AB )

$Q=n C_{p}\;(\large\frac{3T_{0}}{2})$

Work done on the gas during BC

$= nR (2T_{0}) ln (4)$

$w=4nRT_{0} ln(2)$

$\large\frac{d}{w}= \large\frac{nC_{p} (\large\frac{3T_{0}}{2})}{4n RT_{0} ln(2)}$

$=\large\frac{3}{8} \; . \large\frac{5}{2 ln2}=\large\frac{15}{16 ln 2}$

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