**Laws of Thermodynamics**

- Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at a given temperature. The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is given, then the rise in temperature of the gas in B is...?
- This video explains the work done in a thermodynamic process when thermodynamic state of an enclosed gas is changed by applying heat or pressure with help of graphs.
- Two graphs shown in the figure are the two Isotherms at their respective temperatures. Which isotherm has greater temperature?
- This video explains the relation between work done and change in the internal energy considering the change in kinetic energy microscopic articles of an enclosed gas in a thermodynamic process ; along with the conventions used for signs of the energy and wok done.
- A container is divided into two equal compartments by a partition. One compartment has a mixture of gases at 300 K and the other compartment is vacuum. The whole system is thermally insulated from the surroundings. When the partition is removed, the gas expands to occupy the whole volume. Its temperature now will be....?
- This video graphically explains the work done by an enclosed gas in situations where one parameter is retained constant throughout the process with equations.
- This video explains the first law of thermodynamics which governs the change in internal energy of the gas system with respect to heat supplied and work done and its dependence on path of the process; with the help of graphs.
- In a process on an ideal gas, dW = 0 and dQ < 0. Then for the gas (a) the temperature will decrease (b) the volume will increase (c) the pressure will remain constant (d) the temperature will increase.
- This video explains some common thermodynamic processes like isochoric, isobaric and isothermal by using first law of thermodynamics, with the help of graphs.
- Two moles of an ideal gas at a given temperature were cooled isochorically, so that the gas pressure reduced to half. Thereafter, as a result of isobaric process, the gas expands till its temperature becomes To again. What is the total amount of heat absorbed by the gas in this process?
- This video explains the different features, equations and graphs related to work done and change in value of parameters for adiabatic process in which no heat is allowed to enter or leave the system. It also illustrates its comparison with an isothermal process.
- For an ideal gas, which of the following is true? (a) the change in internal energy at the constant pressure when the temperature of n mole of the gas change by ΔT is n Cv ΔT. (b) the change in internal energy of the gas in an adiabatic process is equal in magnitude to the work done by the gas. (c) the internal energy does not change in an isothermal process. (d) no heat is added or removed in an adiabatic process.
- When an ideal gas at pressure P, temperature T and volume V is isothermally compressed to V / n, its pressure becomes Pi. If the gas is compressed adiabatically to V / n, its pressure becomes Pa. The ratio Pi / Pa is..?
- This video explains the different features like work done and change in internal energy of a general polytropic process of which adiabatic process is a special case.
- For various thermodynamic processes like free expansion of gas, expansion and compression with pressure as a function of volume, find if the heat is gained or lost in the process.
- This video explains the derivation of molar heat capacities for different thermodynamic processes considering the path dependence of change in heat and work done.
- When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is...?
- A given amount of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure. The amount of the heat required to raise the temperature of the same gas through the same range at constant volume is...?
- This video explains the work done and change in internal energy fo a cyclic process in which a system attains its initial state after some time, with hep of graphs. It also shows a summary of work done, change in internal energy and heat supplied for every thermodynamic processes discussed so far.
- Figure shows the Pressure-Volume diagram for a fixed mass of an ideal gas undergoing cyclic process. AB represents isothermal process and CA represents adiabatic process. Plot the Pressure-Temperature (P-T) diagram of the cyclic process.
- The following figure shows a cyclic process ABCA on a Volume-Temperature (V-T) diagram. Plot the Pressure-Volume (P-V) for this process.
- An ideal mono-atomic gas is taken around the cycle ABCDA as shown in the Pressure – Volume (P-V) diagram. Find the work done during the cycle.
- The figure shows the Pressure-Volume (P-V) plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semicircle and CDA is half of an ellipse. Then which of the following is true. (a) the process during the path A → B is isothermal (b) work done during the path A→ B→C is zero (c) heat flows out of the gas during the path B→C→D (d) positive work is done by the gas in the cycle ABCDA.
- This video introduces the concept of entropy which is a measure of randomness of a system and helps in understanding the second law of thermodynamics discussed here. It also explains the reversible thermodynamic processes.
- A quantity of heat ΔH is transferred from a large heat reservoir at temperature TH to another large heat reservoir at temperature TL, with TH > TL. The heat reservoirs have such large capacities that there is no observable change in their temperatures. Show that the entropy of the entire system has increased.
- An ideal gas is confined to a cylinder with a movable piston. The piston is slowly pushed in so that the gas temperature remains constant. During the compression, a known amount of work is done on the gas. Find the entropy change of the gas.
- This video discusses the mechanism of heat engine that converts heat into work and its limitations. It also explains the feature of an ideal engine called Carnot engine.
- This video explains in detail the concept of efficiency for Carnot engine and the method to derive the highest theoretical efficiency possible for a Carnot engine.
- Let the temperature of the two heat reservoirs in the ideal Carnot engine is given. Which of these, increasing temperature of source or decreasing temperature of sink would result in a greater improvement in the efficiency of the engine?
- An ideal gas is taken through a cyclic thermodynamic process involving four steps. The amounts of heat involved in these steps are given. The corresponding amounts of work done in three steps are known. The efficiency of the cycle is η. Then find the work done in fourth step.
- Pressure-Volume (P-V) plots for two gases during adiabatic processes are shown in the figure. Plots 1 and 2 correspond respectively to which of the following gases? (a) He and O2 (b) O2 and He (c) He and Ar (d) O2 and N2
- An ideal gas is taken through the cycle A →B → C → A, as shown in the figure. If the net heat supplied to the gas in the cycle is given, the work done by the gas in the process A →B is....?
- An ideal gas having initial pressure P, volume V and temperature T is allowed to expand adiabatically until its volume becomes 5.66 V while its temperature falls to T/2. Find the number of degrees of freedom of gas molecules and work done by the gas during the expansion.
- Two moles of a monoatomic ideal gas occupy a volume V at a given temperature. The gas is expanded adiabatically to a volume 2√2 V. Find the following. (i)The final temperature of the gas. (ii)The change in the internal energy of the gas in this process. (iii)The work done by the gas during the process.
- One mole of an ideal mono atomic gas is taken round the cyclic process A→B→C→A as shown in the figure. Find the following. (i)The work done by the gas. (ii)The heat energy rejected by the gas in the process A→B. (iii)The heat energy rejected by the gas in the process C→A. (iv)The heat energy rejected by the gas in the process B→C.
- Two moles of an ideal gas with volume V, pressure 2P and temperature T undergo a cyclic process A→B→C→D→A as shown in the figure. Find the net work done in the complete cycle.
- Two moles of an ideal monoatomic gas is taken through a cycle A→B→C→A as shown in the Pressure – Temperature (P-T) diagram. During the process A→B, pressure and temperature of the gas vary such that PT = K, where K is a constant. Find the constant K and work done in process A→B. Also find the heat energy released in the process A→B and B→C.
- A sample of given mass of mono-atomic helium ( assumed ideal ) is taken through the process A→B→C and another sample of same mass of the same gas is taken through the process A→D→C as shown in the figure. Find the temperature of state A, B, C and D.
- Two moles of an ideal mono-atomic gas, initially at pressure P1 = P and volume V1 = 2√2 V, undergo an adiabatic compression until its volume is V2 = V and the pressure is P2. Then the gas is given heat Q at constant volume V2. Plot the pressure-volume (P-V) graph of the complete process. Also find the following. (i) pressure P2 (ii) total work done by the gas (iii) change in internal energy due to adiabatic compression and (iv) the temperature T2 of the gas after it is adiabatically compressed.
- Two different adiabatic paths for the same gas intersect two isothermals at T1 and T2 as shown in Pressure-Volume(P-V) diagram. How does ratio of volume at D and A compare by ratio of volume at C and B?
- Two moles of helium gas are initially at a given temperature and volume. The gas is first expanded at constant pressure until the volume is doubled. Then it undergoes an adiabatic change until the temperature returns to its initial value. Sketch the process on a Pressure-Volume (P-V) diagram. What are the final volume and pressure of the gas? What is the work done by the gas?
- 2 moles of a mono-atomic ideal gas is taken through a cyclic process starting from A as shown in the figure. Given ratios of volume at B & A and D & A along with temperature at A. Find the following. (i) temperature of gas at point B (ii) total work done by the gas and the heat absorbed in complete cycle.
- One mole of a diatomic ideal gas is taken through a cyclic process starting from point A. The process A→B is an adiabatic compression, process, B→C is an isobaric expansion, C→D is an adiabatic expansion and process D→A is isochoric. The volume ratios at A&B and C&B and the temperature at A is given. Calculate the temperature of gas at points B and D.
- Three moles of an ideal gas at pressure PA and temperature TA are isothermally expanded to twice the original volume. The gas is then compressed at constant pressure to its original volume. Finally the gas is heated at constant volume to its original pressure PA. Plot Pressure – Volume (P-V) and Pressure - Temperature graph for the complete process. Also find the net work done and net heat supplied during the complete process.
- Two identical containers A and B fitted with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The mass of the gas in A and that in B is known. The gas in each cylinder is now allowed to expand isothermally to the same final volume 2V. The change in pressure in A and B are found to be ΔP and 1.5 ΔP respectively. Then find the ratio of mass of gases in A and B.
- An ideal gas is taken from state A (pressure P, volume V) to state B (pressure P/2, Volume 2V) along a straight line in the P-V diagram as shown in the figure. Then which of the following is correct. (a) the work done by the gas in the process A to B exceeds the work that would be done by it if the system were taken from A to B along the isotherm. (b) in the T-V diagram, the path AB becomes a part of a parabola. (c) in the P-T diagram, the path AB becomes a part of a hyperbola. (d) in going from A to B, the temperature T of the gas first increases to a maximum and then decreases.
- A weightless piston divides a thermally insulated cylinder into two parts of volumes V and 3V. 2 moles of ideal gas at pressure P = 2 atmosphere are confined to the part with volume V = 1 litre. The remainder of the cylinder is evacuated. Initially the gas is at room temperature. The piston is now released and the gas expands to fill the entire space of the cylinder. The piston is then pressed back to the initial position. Find the increase of internal energy in the process and final temperature of the gas. The ratio of the specific heat of the gas is given.
- A small spherical mono-atomic ideal gas bubble is trapped inside a liquid of given density. Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T1, the height of the liquid is H and the atmospheric pressure is Po (Neglect surface tension). Find the forces acting on the bubble other than buoyancy. Also find the buoyancy force acting on bubble and its temperature at a height from the bottom.
- A box shown in figure has a partition that can slide without friction along the length of the box. Initially, each of the two chambers of the box has one mole of a monatomic ideal gas at a pressure Po, volume Vo and temperature To. The chamber on the left is slowly heated by an electric heater. The walls of the box and the partition are thermally insulated. The gas in the left chamber expands, pushing the partition until the final pressure in both chambers become 243Po / 32. Determine : (i) final temperature of gas in each chamber and (ii) the work done by the gas in the right chamber.
- 3 moles of an ideal gas initially at temperature To = 273 K were isothermally expanded so that its volume Vo increases 5 times. It is then heated at constant volume till the final pressure becomes equal to its initial pressure Po. If the total heat supplied to the gas during the entire process is given, find the adiabatic constant g for this gas.
- One mole of an ideal gas expands in such a way that its pressure P varies with its volume V according to P = α V, where α is a constant. If the final volume of the gas is η times that of the initial, find the increase in its internal energy and the molar heat capacity of the gas. The ratio of the two specific heats of the gas is known.
- One mole of an ideal gas having known adiabatic exponent expands in such a way that the amount of heat transferred to the gas equals the decrease in its internal energy. Find the molar heat capacity C of the gas in this process, the equation relating its temperature and volume, and the work performed by the gas when its volume increases η times, assuming the initial temperature of the gas to be To.
- Consider one mole of an ideal gas whose temperature varies with volume as T = T0 + αV, where T0 and α are constants. Assuming the molar heat capacity of the gas at constant pressure to be Cp, find molar heat capacity of the gas as a function of its volume and the amount of heat transferred to the gas if its volume increases from Vi to Vf.
- The molar heat capacity of an ideal gas, having an adiabatic exponent varies with temperature as c =α/T where α is a constant. Find the work performed by one mole of this gas during its heating from temperature To to a temperature η times higher, and the equation of the process in the variables P, V.
- The pressure in a monatomic gas increases linearly when its volume is increased. Calculate the molar heat capacity of the gas.
- A gaseous mixture enclosed in a vessel of volume V consists of one gram mole of a gas A and another gas B with given adiabatic exponent at a certain temperature T. The gases A and B do not react with each other and are assumed to be ideal. The gaseous mixture follows the equation PV19/13 = constant, in adiabatic processes. (a) Find the number of gram mole of the gas B in the gaseous mixture. (b) Compute the speed of sound in the gaseous mixture at a given temperature. (c) If T is raised by 1 K from 300 K, find the percentage change in the speed of sound in the gaseous mixture. (d) The mixture is compressed adiabatically to 1/5 of its initial volume V. Find the change in its adiabatic compressibility in terms of the given quantities.
- A cycle consists of two isochoric and two adiabatic lines as shown in figure. Find the efficiency of this cycle if the volume of the ideal gas changes 10 times within the cycle. Take the working substance to be nitrogen.
- A cycle consists of two isobaric and two adiabatic lines as shown in figure. Assuming the working substance to be an ideal gas with given adiabatic exponent, find the efficiency of the cycle if the pressure changes n times within the cycle.