Why is the P-V curve for an adiabatic process steeper than that f… - Vidyadip

Question

Why is the $P-V$ curve for an adiabatic process steeper than that for an isothermal process ?

✓

Answer

Adiabatic process : $PV^γ$ = constant
$\therefore V^γdP + γPV^{γ-1} dV = 0$
$ \therefore V^\gamma dP +\gamma PV { }^{\gamma-1} dV =0$
$\therefore \frac{d P}{d V}=-\frac{\gamma P}{V} $
Isothermal process: $P V=$ constant
$\therefore pdV + VdP =0 \therefore \frac{d P}{d V}=\frac{P}{-V}$
$NoW _1 Y>1$
$\therefore\left|\left(\frac{d P}{d V}\right)_{\text {adiabatic }}\right|>\left|\left(\frac{d P}{d V}\right)_{\text {isotherm }}\right|$
$\therefore \frac{d P}{d V}$ is the slope of the $P - V$ curve.
$\therefore $The $P – V$ curve for an adiabatic process is steeper than that for an isothermal process.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Short Answer Type Question" from Thermodynamics→Thermodynamics — all question types→Physics STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

When stationary waves of wavelength $40 cm$ are formed in a medium, what is the distance between
1. successive nodes
2. a node and the next antinode?

The capacitance of a parallel-plate air capacitor is $2\ pF$. If the air is replaced by a medium of dielectric constant $10.$ What will be its capacitance?

Define: Junction

What is a Light Emitting Diode? Draw its circuit symbol.

The capacitance of a charged capacitor is $C$ and the energy stored in it is $U$. What is the value of the charge on the capacitor?

State with reason if the statement is true or false : A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling) motion.

What is the property of a system or a system variable?

To start a pendulum swinging, usually you pull it slightly to one side and release it. What kind of energy is transferred to the mass in doing this?

A driver pushes the brake pedal of a car exerting a force of $100 \mathrm{~N}$ that is increased by the simple lever to a force of $500 \mathrm{~N}$ on the pedal (master) cylinder. The hydraulic system transmits this force to the four wheel (slave) cylinders. If the pedal cylinder has a diameter of $0.5 \mathrm{~cm}$ and each wheel cylinder has a diameter of $2.5 \mathrm{~cm}$, calculate the magnitude of the force $F_5$ on each of the wheel cylinder.

A straight conductor is moving with a velocity of \(3 m / s\), at right angles to a magnetic field \(4.5 \times 10^{-5} Wb / m ^2\). If an e. m. f. developed between its ends is \(1.35 \times 10^{-4}\) volt, calculate the length of straight conductor.