An ideal gas equation can be written as $\mathrm{P}=\frac{\mathrm{\rho RT}}{{\mathrm{M}}_0}$ where $\mathrm{\rho }$ and ${\mathrm{M}}_0$ are respectively:

1.	mass density, the mass of the gas
2.	number density, molar mass
3.	mass density, molar mass
4.	number density, the mass of the gas

If \(C_p\) and \(C_v\) denote the specific heats (per unit mass) of an ideal gas of molecular weight \(M\) (where \(R\) is the molar gas constant), the correct relation is:
1. \(C_p-C_v=R\)
2. \(C_p-C_v=\frac{R}{M}\)
3. \(C_p-C_v=MR\)
4. \(C_p-C_v=\frac{R}{M^2}\)

A cylinder of fixed capacity \(44.8\) litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by \(15.0^\circ~\mathrm{C}?\) (\(R=8.31\) J mol^–1 K^–1)

A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of $500 {\mathrm{ms}}^{-1}$ in the vertical direction. The pressure of the gas inside the vessel as observed by us on the ground:

Which of the following diagrams (figure) depicts ideal gas behaviour?

1. (a), (c)
2. (a), (d)
3. (c), (d)
4. (a), (b)

Match Column - I and Column - II and choose the correct match from the given choices.
 

Which of the following parameters is the same for molecules of all gases at a given temperature?

The process on an ideal gas as shown in the figure given below is:
             

1. isothermal
2. isobaric
3. isochoric
4. none of these