A) \[{{X}_{c}}={{X}_{m}}={{X}_{g}}\]
B) \[{{X}_{c}}>{{X}_{m}}>{{X}_{g}}\]
C) \[{{X}_{c}}<{{X}_{m}}<{{X}_{g}}\]
D) \[{{X}_{m}}<{{X}_{c}}<{{X}_{g}}\]
Correct Answer: C
Solution :
\[\frac{Q}{At}=K\frac{\Delta \theta }{l}\]Þ \[K\frac{\Delta \theta }{l}\]= constant Þ \[\frac{\Delta \theta }{l}\propto \frac{1}{K}\] Hence If \[{{K}_{c}}>{{K}_{m}}>{{K}_{g}}\], then \[{{\left( \frac{\Delta \theta }{l} \right)}_{c}}<{{\left( \frac{\Delta \theta }{l} \right)}_{m}}<{{\left( \frac{\Delta \theta }{l} \right)}_{g}}\Rightarrow {{X}_{c}}<{{X}_{m}}<{{X}_{g}}\] because higher K implies lower value of the temperature gradient.
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