Physics · Kinetic Theory · NEET
It depends on which two variables you plot. On a P-V graph the temperature T is fixed, so P = (nRT)/V = constant/V. Here P and V multiply to a constant, so as V grows P shrinks. This shape is a rectangular hyperbola, which is a curve. On a T-V graph the pressure is fixed, so T = (P/nR) V, which is 'T equals a constant times V'. That is the equation of a straight line through the origin. Same for P-T at fixed volume: P = (nR/V) T, again a straight line through the origin. So a curve appears only when the two plotted quantities are multiplied together (P and V); when one is a constant multiple of the other, you get a straight line.
Use T = (P/nR) V. The number in front of V is the slope, and it equals P/nR. So the slope is directly proportional to pressure. The steeper the line, the higher the pressure. If three isobars P1, P2, P3 are drawn and P1 is the steepest while P3 is the flattest, then P1 > P2 > P3. This exact idea was tested in NEET 2024. Warning: some students look at where the line is 'higher up' on the graph instead of its steepness. Always compare slopes, not heights.
They are three ways to hold one variable constant. Isotherm means constant temperature (iso = same, therm = heat): it is the P-V curve, a hyperbola. Isobar means constant pressure (bar = pressure): it is the T-V straight line through the origin. Isochore means constant volume (chore = space): it is the P-T straight line through the origin. Simple memory trick: therm-Temperature-fixed gives the Curve; the other two give straight lines. Higher-temperature isotherms sit farther from the origin on a P-V graph.
For an ideal gas at fixed volume, P = (nR/V) T, so when T = 0 K the pressure P = 0. The straight line therefore passes exactly through the origin, and T here must be in kelvin. Students get tricked when the graph uses Celsius: in Celsius the line does not pass through (0,0), it hits the axis near -273 degrees C. So on a kelvin axis it goes through the origin; on a Celsius axis it does not. Real gases also deviate at very low temperature because they liquefy, but for the ideal-gas assumption in NEET the kelvin line is straight through zero.
For each isotherm PV = nRT = constant. A larger T gives a larger value of PV, so that curve sits farther away from the origin (up and to the right). If two isotherms never cross, the one farther from the origin is the hotter one. Pick any vertical line (a fixed V) and read both pressures: the curve with higher P at that same V has the higher temperature, because PV is bigger.
The T-V curves of an ideal gas (T is temperature, V is volume) are drawn at three pressures P1, P2 and P3, and compared with Charles's law lines shown dotted. The correct relation between the pressures is:
A gas has an r.m.s. velocity of 200 m/s at 27 degrees C and 1.0 x 10^5 N/m^2 pressure. When the temperature and pressure become 127 degrees C and 0.05 x 10^5 N/m^2 respectively, the r.m.s. velocity of its molecules (in m/s) is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is a curve, specifically a rectangular hyperbola. At fixed temperature PV = constant, so P = constant/V. As volume rises, pressure falls along a smooth curve, never a straight line.
A straight line through the origin when temperature is in kelvin, because P = (nR/V) T. Its slope nR/V is larger when the volume is smaller.
Plotting v_rms against root T gives a straight line through the origin, since v_rms is proportional to root T. Plotting v_rms against T directly gives a curve that rises more slowly as T grows.
Because PV = nRT, a larger T means a larger product PV. So at any given volume the pressure is higher, pushing the whole curve up and to the right, away from the origin.
Only approximately. At high pressure or low temperature real gases deviate, and the P-T line bends because the gas can liquefy. For NEET ideal-gas questions, treat the lines as straight through the origin in kelvin.
