PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Physics

An ideal gas at pressure 2.5 × 10⁵ Pa and temperature 300 K occupies 100 cc. It is adiabatically compressed to half its original volume. Calculate (a) the final pressure (b) the final temperature and (c) the work done by the gas in the process. Take γ = 1.5

Consider a given sample of an ideal gas (C_p/C_v = γ) having initial pressure p₀ and volume V₀. (a) The gas is  isothermally taken to a pressure p₀/2 and from there, adiabatically to a pressure p₀/4. Find the final volume. (b) The gas is brought back to its initial state. It is adiabatically taken to a pressure p₀/2 and from there, isothermally to a pressure p₀/4. Find the final volume.

Two samples A and B, of the same gas have equal volumes and pressures. The gas in sample A is expanded isothermally to double its volume and the gas in B is expanded adiabatically to double its volume. If the work done by the gas is the same for the two cases, show that γ satisfies the equation 1 − 2^1−γ = (γ − 1) ln2.

1 litre of an ideal gas (γ = 1.5) at 300 K is suddenly compressed to half its original volume. (a) Find the ratio of the final pressure to the initial pressure. (b) If the original pressure is 100 kPa, find the work done by the gas in the process. (c) What is the change in internal energy? (d) What is the final temperature? (e) The gas is now cooled to 300 K keeping its pressure constant. Calculate the work done during the process. (f) The gas is now expanded isothermally to achieve its original volume of 1 litre. Calculate the work done by the gas. (g) Calculate the total work done in the cycle.

Figure shows a cylindrical tube with adiabatic walls and fitted with an adiabatic separator. The separator can be slid into the tube by an external mechanism. An ideal gas (γ = 1.5) is injected in the two sides at equal pressures and temperatures. The separator remains in equilibrium at the middle. It is now slid to a position where it divides the tube in the ratio 1 : 3. Find the ratio of the temperatures in the two parts of the vessel.

Two vessels A and B of equal volume V₀ are connected by a narrow tube that can be closed by a valve. The vessels are fitted with pistons that can be moved to change the volumes. Initially, the valve is open and the vessels contain an ideal gas (C_p/C_v = γ) at atmospheric pressure p₀ and atmospheric temperature T₀. The walls of vessel A are diathermic and those of B are adiabatic. The valve is now closed and the pistons are slowly pulled out to increase the volumes of the vessels to double the original value. (a) Find the temperatures and pressures in the two vessels. (b) The valve is now opened for sufficient time so that the gases acquire a common temperature and pressure. Find the new values of the temperature and pressure.

The figure shows an adiabatic cylindrical tube of volume V₀ divided in two parts by a frictionless adiabatic separator. Initially, the separator is kept in the middle, an ideal gas at pressure p₁ and temperature T₁ is injected into the left part and another ideal gas at pressure p₂ and temperature T₂ is injected into the right part. C_p/C_v = γ is the same for both the gases. The separator is slid slowly and is released at a position where it can stay in equilibrium. Find (a) the volumes of the two parts (b) the heat given to the gas in the left part and (c) the final common pressure of the gases.

An ideal gas of density 1.7 × 10⁻³ g cm⁻³ at a pressure of 1.5 × 10⁵ Pa is filled in a Kundt's tube. When the gas is resonated at a frequency of 3.0 kHz, nodes are formed at a separation of 6.0 cm. Calculate the molar heat capacities C_p and C_v of the gas.

The normal duration of I.Sc. Physics practical period in Indian colleges is 100 minutes. Express this period in microcenturies. 1 microcentury = 10⁻⁶ × 100 years. How many microcenturies did you sleep yesterday?

The frequency of vibration of a string depends on the length L between the nodes, the tension F in the string and its mass per unit length m. Guess the expression for its frequency from dimensional analysis.

Give example where  the velocity of a particle is zero but its acceleration is not zero.

Give example where the velocity is opposite in direction to the acceleration.

Give example where the velocity is perpendicular to the acceleration.

 In figure shows the x coordinate of a particle as a function of time. Find the sings of v_x and a_x at t = t₁, t = t₂ and t = t₃.

A stone is released from an elevator going up with an acceleration a. The acceleration of the stone after the release is 

The length and the radius of a cylinder measured with a slide callipers are found to be 4.54 cm and 1.75 cm respectively. Calculate the volume of the cylinder.

The length of the string of a simple pendulum is measured with a metre scale to be 90.0 cm. The radius of the bod plus the length of the hook is calculated to be 2.13 cm using measurements with a slide callipers. What is the effective length of the pendulum? (The effective length is defined as the distance between the point of suspension and the centre of the bob.)

The accelerations of a particle as seen from two frames S₁ and S₂ have equal magnitude 4 m/s².