A) np
B) \[{{p}^{1/n}}\]
C) \[\frac{p}{n}\]
D) \[{{p}^{n}}\]
Correct Answer: C
Solution :
| [c]\[V{{p}^{n}}=\,\text{constant}\] |
| \[V{{p}^{n}}=\,(V\,+\Delta V)\,{{(p+\,\Delta p)}^{n}}\] |
| \[=V{{p}^{n}}\,\left( 1+\,\frac{\Delta V}{V} \right)\,\,\left( 1+\,n\,\frac{\Delta p}{p} \right)\] |
| \[1=\,1+\frac{\Delta V}{V}+\,n\frac{\Delta p}{p}+\,\frac{n\,\Delta V}{V}\,\,.\,\frac{\Delta p}{p}\] |
| \[\frac{\Delta V}{V}=-n\,\frac{\Delta p}{p}\] |
| \[\therefore \] \[k=\frac{-\Delta p}{\Delta V/V}\,\,=\,\frac{p}{n}\] |
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