If the pressure P and volume V of a gas are connected by the relation PV^1 / 4=C where, C is a c

step 1 To solve the problem, that is to find the percentage increase in pressure if there is a decrease

If the pressure P and volume V of a gas are connected by the...

If the pressure $\mathrm{P}$ and volume $\mathrm{V}$ of a gas are connected by the relation $\mathrm{PV}^{1 / 4}=\mathrm{C}$ where, $\mathrm{C}$ is a constant, then the percentage increase in the pressure corresponding to a decrease of $\frac{1}{2} \%$ in the volume is (a) $\frac{1}{4} \%$ (b) $\frac{1}{8} \%$ (c) $\frac{1}{2} \%$ (d) $1 \%$

If the pressure $\mathrm{P}$ and volume $\mathrm{V}$ of a gas are connected by the relation $\mathrm{PV}^{1 / 4}=\mathrm{C}$ where, $\mathrm{C}$ is a constant, then the percentage increase in the pressure corresponding to a decrease of $\frac{1}{2} \%$ in the volume is
(a) $\frac{1}{4} \%$
(b) $\frac{1}{8} \%$
(c) $\frac{1}{2} \%$
(d) $1 \%$

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Key Concepts

Polytropic Process

A polytropic process in thermodynamics is one in which pressure and volume are related by the equation PV^n = constant, where n is the polytropic index. This concept generalizes several fundamental thermodynamic processes and is useful for analyzing how gases behave under different types of compression or expansion beyond isothermal or adiabatic conditions.

Differential Calculus in Physical Relationships

Differential calculus is used to approximate how small changes in one variable affect another when the variables are related by a continuous function. In physics, especially in processes described by power law relationships, differentials help in determining the proportional variations between the quantities, enabling a simplified analysis of percentage changes.

Percentage Change Calculation

Percentage change is a method to quantify the relative variation in a quantity compared to its initial value. It is particularly useful in physics when assessing how a small change in one variable, such as volume in a thermodynamic process, leads to a corresponding change in another variable, like pressure. This concept is central to understanding the sensitivity of physical systems to perturbations.

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