Class 11th

For one mole of an ideal gas, which of these statements must be true?
(a) U and H each depends only on temperature
(b) Compressibility factor z is not equal to 1
(c) Cp,m – Cv,m = R
(d) dU = CvdT for any process

The change in the magnitude of the volume of an ideal gas when a small additional pressure ΔP is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity ΔT at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm. respectively. If |ΔT| = C|ΔP| then value of C in (K/atm) is ….

The linear mass density of a thin rod AB of length L varies from A to B as λ(x) = λ₀ (1 + x/L), where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:

The speed verses time graph for a particle is shown in the figure. The distance travelled (in m ) by the particle during the time interval t = 0 to t = 5 s will be .

In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as:

A cube of metal is subjected to a hydrostatic pressure 4GPa. The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, B = 8 * 10¹⁰ Pa)

Match the thermodynamics processes taking place in a system with the correct conditions. In the table: ΔQ is the heat supplied, ΔW is the work done and ΔU is change in internal energy of the system. Match the following:

When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by y(t) = y₀sin² ωt, where ' y ' is measured from the lower end of unstretched spring. Then ω is:

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv² where v is it speed. The maximum height attained by the ball is:

A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms⁻¹ at a point where the pressure is P Pascal. At another point where pressure is P/2 Pascal its speed is V ms⁻¹. If the density of the fluid is ρ kgm⁻³ and the flow is streamline, then V is equal to: