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Which of the following statement is correct regarding \(p-V\) graph?
1. Slope of \(p-V\) graph in an isothermal process is \(-\frac{p}{V}\).
2. Slope of \(p-V\) graph in an adiabatic process is \(-\frac{p}{V}\).
3. Slope of \(p-V\) graph in an isochoric process is \(-\frac{\gamma p}{V}\).
4. Slope of \(p-V\) graph in an isobaric process is zero.
Options:
1. Slope of \(p-V\) graph in an isothermal process is \(-\frac{p}{V}\).
2. Slope of \(p-V\) graph in an adiabatic process is \(-\frac{p}{V}\).
3. Slope of \(p-V\) graph in an isochoric process is \(-\frac{\gamma p}{V}\).
4. Slope of \(p-V\) graph in an isobaric process is zero.
Solution:
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Verified Answer
The correct answer is:
1, 4 are correct
(i) and (iv) options are correct.
(i) Slope of \(p-V\) graph in an isothermal process is \(-\frac{p}{V}\) this is correct.
For isothermal process, slope of \(p-V^{\prime}\) curve \(\frac{d p}{d V}=-\frac{p}{V}\)
(ii) Slope of \(p-V\) group in an adiabatic process is \(-\frac{p}{V}\), which is wrong.
Because slope of \(p-V\) graph in an adiabatic process is \(-\frac{\gamma p}{V}\).
(iii) Slope of \(p\) - \(V\) graph in an isochoric process is \(-\frac{\gamma p}{V}\) this option is wrong.
Because slope of \(p-V\) graph for isochoric process is
\(\frac{d p}{-\frac{d V}{V}}-\frac{d V}{V}=\frac{d p}{0}=\infty\)
(d) Slope of \(p-V\) graph in an isobaric process is zero. This option is correct.
\(p-V\) curve is a straight line parallel to volume axis, slope of \(p\) - \(V\) curve for an isobaric process
\(\frac{d p}{d V}=0.\)
(i) Slope of \(p-V\) graph in an isothermal process is \(-\frac{p}{V}\) this is correct.
For isothermal process, slope of \(p-V^{\prime}\) curve \(\frac{d p}{d V}=-\frac{p}{V}\)
(ii) Slope of \(p-V\) group in an adiabatic process is \(-\frac{p}{V}\), which is wrong.
Because slope of \(p-V\) graph in an adiabatic process is \(-\frac{\gamma p}{V}\).
(iii) Slope of \(p\) - \(V\) graph in an isochoric process is \(-\frac{\gamma p}{V}\) this option is wrong.
Because slope of \(p-V\) graph for isochoric process is
\(\frac{d p}{-\frac{d V}{V}}-\frac{d V}{V}=\frac{d p}{0}=\infty\)
(d) Slope of \(p-V\) graph in an isobaric process is zero. This option is correct.
\(p-V\) curve is a straight line parallel to volume axis, slope of \(p\) - \(V\) curve for an isobaric process
\(\frac{d p}{d V}=0.\)
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