P-T diagram of an ideal gas having three different densities _1,...

P-T diagram of an ideal gas having three different densities

\rho_1, \rho_2, \rho_3

(in three different cases) is shown in the figure. Which of the following is correct : P-T diagram of an ideal gas having three different densities _1, _2, _3 (in three different cases) is shown in the

P-T diagram of an ideal gas having three different densities _1, _2, _3 (in three different cases) is shown in the

Options

A $\rho_1>\rho_2$
B $\rho_2 < \rho_3$
C $\rho_1=\rho_2=\rho_3$
D $\rho_1 < \rho_2$

Correct answer

A. $\rho_1>\rho_2$

Step-by-step solution

For ideal gas

\begin{aligned} & P V=n R T \\ & P V=\frac{m}{M} R T \\ & P=\left(\frac{M}{V}\right) \frac{R T}{M} \\ & P=\frac{\rho R T}{M} \end{aligned}

(Where

\mathrm{m}

is mass of gas and

\mathrm{M}

is molecular mass of gas) P-T diagram of an ideal gas having three different densities _1, _2, _3 (in three different cases) is shown in the

for same temperature

\mathrm{P}_1>\mathrm{P}_2>\mathrm{P}_3

\rho_1>\rho_2>\rho_3

Practice Thermodynamics on Quantrex Academy →

More from Thermodynamics

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process ( ab )… JEE Advanced 2026 As shown in the figure, five Carnot engines, each with efficiency η and same number of… JEE Advanced 2026 Ten moles of an ideal monoatomic gas, initially in state a at atmospheric pressure and… JEE Advanced 2026 One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston… JEE Main 2026 Initial pressure and volume of a monoatomic ideal gas are P and V . The change in… JEE Main 2026 A cylinder with adiabatic walls is closed at both ends and is divided into two… JEE Main 2026 Two closed vessels of same volume are joined through a narrow tube and both vessels are… JEE Main 2026 A certain gas is isothermally compressed to ((1)/(3))^ rd of its initial volume ( V_o = 3… JEE Main 2026 Full Thermodynamics list All JEE Main PYQs