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If we plot a graph between volume V and inverse of pressure P (i.e., 1

June 1, 2025 by rawan239

If we plot a graph between volume V and inverse of pressure P (i.e., 1/P) for an ideal gas at constant temperature T, the curve so obtained is:

straight line

circle

parabola

hyperbola

This question was previously asked in

UPSC NDA-2 – 2016

Download PDF Attempt Online

A graph between volume V and inverse of pressure (1/P) for an ideal gas at constant temperature T is a straight line.

According to the Ideal Gas Law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. For a fixed amount of gas (n is constant) at a constant temperature (T is constant), the product nRT is a constant. Let’s call this constant C. So, PV = C (This is Boyle’s Law). We want to plot V against 1/P. Rearranging the equation, we get V = C * (1/P). If we let Y = V and X = 1/P, the equation becomes Y = CX. This is the equation of a straight line passing through the origin with slope C (which is equal to nRT).

Plotting V versus P directly would yield a hyperbola (PV = C). A parabola is typically associated with quadratic relationships, and a circle with relationships involving the sum of squares.

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