CBSE Class 12 Physics Heat and Thermodynamics Advanced Problems

CBSE Class 12 Physics Heat and Thermodynamics Advanced Problems. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

1. The rectangular box shown in the figure has a partition which can slide without friction along the length of the box. Initially, each of the chambers of the box has one mole of a monoatomic ideal gas (γ = 5/3) at a pressure p₀, volume V₀ and temperature T_0. The chamber on the left is slowly heated. The walls of the box and the partition are thermally insulated. Heat loss through the lead wires of the heater is negligible. The gas in the left chamber expands, pushing the partition until the final pressure in both becomes 243/32 p₀. Determine:

(a) the final temperature of the gas in each chamber;
(b) the work done by the gas in the right chamber.

2. Heat flows radially outward through a cylindrical insulator of outside radius R₂ surrounding a steam pipe of radius R₁. The temperature of the inner surface of the insulator is T₁, that of the outer surface is T₂. At what radial distance from the centre of the pipe is the temperature just halfway between T₁ and T₂?

3. Heat flows radially outward through a spherical shell of outside radius R₂ and inner radius R₁. The temperature of the inner surface of the shell is θ₁, that of the outer surface is θ₂. At what radial distance from the centre of the shell is the temperature just halfway between and θ₁ and θ₂?

4. A smooth vertical tube with two different sections is open at both ends and equipped with two pistons of different areas. Each piston slides within a particular tube section. One mole of an ideal gas is enclosed between the pistons which are tied with a non-stretchable thread. The cross-sectional area of the upper piston is greater than that of the lower piston by ΔS = 10 cm². The combined mass of the pistons is equal to 5 kg. The outside pressure of air is p0 = 1 atm.By how many kelvins must the gas between the pistons be heated to shift the pistons through l = 5 cm?

5. 2.00 moles of a monatomic ideal gas (U = 1.5 nRT) is enclosed in an adiabatic, vertical cylinder fitted with a smooth, light adiabatic piston. The piston is connected to a vertical spring of spring constant 200 N/m as shown in figure. The area of cross-section of the cylinder is 20.0cm². Initially, the spring is at its natural length and the temperature of the gas is 300 K. The atmospheric pressure is 100 kPa. The gas is heated slowly for some time by means of an electric heater so as to move the piston up through 10 cm. Find

(a) the work done by the gas
(b) the final temperature of the gas and
(c) heat supplied by the heater.

6. Pressure-temperature (P-T) graph of n moles of an ideal gas in shown in figure. Plot the corresponding
(a) density-volume (ρ-V) graph
(b) pressure-volume (P-V) graph and
(c) density-pressure (ρ-P) graph.

7. Two moles of a monoatomic ideal gas undergo a cyclic process ABCDA as shown in figure. BCD is a semicircle. Find the efficiency of the cycle. A

8. Three moles of an ideal gas initially at temperature T = 273 K is expanded isothermally so that its volume
increases 5 times. It is then heated at constant volume till the final pressure becomes equal to its initial
value. If the total amount of heat transferred is Q = 80 kJ. Find the ratio γ  C_pC_v= of the gas.

9. Two samples A and B of same gas have equal volumes and pressures. The gas in sample A is expanded isothermally to double its volume and the gas in sample B is expanded to double its volume adiabatically. If work done by the gas is same in the two processes. Show that γ(=Cp/Cv) satisfies the equation 1 – 2^1–γ = (γ –1)ln 2.

10. Two identical adiabatic vessels A and B, each containing n moles of a monoatomic and diatomic ideal gas respectively, are connected by a rod of length l and cross-sectional area A. Thermal conductivity of rod is K and lateral surface of the rod is insulated. At time t = 0, temperature of the gases in the vessel are T₁ and T₂ respectively with T₁ > T₂. Find the temperature difference between the vessels at any time t.

11. A monoatomic ideal gas of two moles is taken through a cyclic process starting from A as shown in the figure. The volume ratios are 2V_A/V_B = and4 V_D/V_A = If the temperature T^A at A is 27°C, calculate

(a) the temperature of the gas at point B. TB
(b) heat absorbed or released by the gas in each process.
(c) the total work done by the gas during the complete cycle.
Express your answer in terms of the gas constant R.

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