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Thermodynamics

# The ratio of molar heat capacities in path 1 and path 2

$(a)\;< 1\qquad(b)\; > 1\qquad(c)\;=1\qquad(d)\;zero$

Answer : $\;< 1$
Explanation :
Path 1 : $\;dQ_{1}=du_{1}+dv$
$\bigtriangleup Q_{1} =\bigtriangleup u_{1} + \bigtriangleup w_{1}$
Path 2 : $\;\bigtriangleup Q_{2}=\bigtriangleup u_{2}+\bigtriangleup w_{2}$
Since for both the paths , the initial and final states are the same , $\;\bigtriangleup u\;$ is the same
$\bigtriangleup Q_{2} > \bigtriangleup Q_{1}$
$nC_{2} \bigtriangleup T > n C_{1} \bigtriangleup T$
$\large\frac{C_{1}}{C_{2}} < 1$