CBSE Class 12 Physics Heat and Thermodynamics Basic Problems

CBSE Class 12 Physics Heat and Thermodynamics Basic 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. A cylinder closed at both ends is separated into two equal (42 cm each) parts by a piston impermeable to heat. Both the parts contain the same masses of a gas at a temperature of 27° C and a pressure of 1 atm. How much should the gas in one part of the cylinder be heated to shift the piston by 2 cm? Find the pressure of the gas after the shifting of the piston.

2. A tall cylindrical vessel with gaseous nitrogen is located in the gravitational field. The temperature of the gas varies with height h in such a way that its density is the same throughout the volume. Find the temperature gradient.

3. A horizontal cylinder closed at one end is rotated with a constant angular velocity ω about a vertical axis passing through the open end of the cylinder. The outside pressure is p₀, the absolute temperature is T and the molar mass of air is M. Find the air pressure as a function of the distance r from the axis of rotation. The molar mass is assumed to be independent of r.

4. An ideal gas at 300 K occupies a volume of 0.5 m³ at a pressure of 2 atm. The gas expands adiabatically until its volume is 1.2 m³. Next, the gas is compressed isobarically to its original volume. Finally, the pressure is increased isochorically until the gas returns to its initial state. Represent the change on the p-V diagram. Determine the temperature at the end of each transformation, and the work done during the cycle. Assume γ = 1.4.

5. Five moles of neon gas (molecular weight = 20) at 2 atm and 27° C is adiabatically compressed to one third its initial volume. Find the final pressure, the temperature and the work done on the gas.

6. One mole of certain ideal gas is contained under the weightless piston of a vertical cylinder at a temperature T. The space over the piston opens into the atmosphere of pressure p₀. What work has to be done in lifting the piston so that the volume of the gas under the piston increases isothermally n times?

7. As a result of the isobaric heating by ΔT = 72 K one mole of a certain ideal gas receives heat Q = 1.6 kJ. Find the work performed by the gas, the increment of its internal energy and the value of its adiabatic exponent γ.

8. A reversible heat engine carries 1 mole of an ideal monoatomic gas around the cycle 1-2-3-1. Process 1-2 takes place at constant volume, process 2-3 is adiabatic and process 3-1 takes place at constant pressure. Compute the values for the heat Δ Q, the change in internal energy ΔU, and the work done ΔW, for each of the three processes and for the cycle as whole. O Vp1(300 K)2(600 K)3(455 K).

9. One mole of argon expands polytropically, the polytropic constant being 1.5, that is, according to the law p^V1.5 = constant. In the process, its temperature changes by ΔT = –26 K. Find
(a) the amount of heat obtained by the gas, and
(b) the work performed by the gas.

10. An ideal gas expands adiabatiacally from an initial temperature T₁ to a final temperature T₂. Prove that the work done by the gas is C_v(T₁ – T₂).

11. Ten grams of oxygen is heated at constant atmospheric pressure from 27°C to 127°C. How much heat is transferred to the oxygen? What fraction of the heat is used to increase the internal energy of the oxygen.

12. Three rods of material x and two rods of material y are connected as shown in the figure here. All the rods are identical (each 1 m long and of cross-sectional area 100 cm²). At the junctions A and C, there are two sources of heat of 25 W and 100 W, and at B and at D there are two sinks maintained at 30°C and 10°C, respectively. Calculate the temperatures of the points A and C is the steady stae. The thermal conductivity of x is 200 J s^–1 m–1K^–1 and that of y is 400 J s^–1 m^–1 K^–1.

13. A cylindrical block of length l = 0.4 m and area of cross-section A = 0.04 m² is placed coaxially on a thin metal disc of mass m = 0.4 kg of the same cross section. The upper face of the cylinder is maintained at a constant temperature T = 400 K and the initial temperature of the disc is T0 = 300 K. If the thermal conductivity of the material of the cylinder is λ = 10 W m–1K–1 and the specific heat of the material of the disc is s = 600 J kg–1 – K–1, how long will it take for the temperature of the disc to increase to T1 = 350 K? Assume for purposes of calculation that the thermal conductivity is very high and that the system is thermally insulated except for the upper face of the cylinder.

14. An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross-section 8.0 × 10^–3 m². Initially the gas is at 300 K and occupies a volume of 2.4 × 10^–3 m³ and the spring is in its relaxed state. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. Calculate the final temperature of the gas. The force constant of the spring is 8000 N/m, and the atmospheric pressure is 1.0 × 105 N/m². The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. Neglect and heat loss through the lead wires of the heater. The heat capacity of the heater coil is negligible.

15. Figure shows a process ABCA performed on n moles of an ideal gas. Find the net heat given to the system during the process.

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