Introduction to Thermodynamic processes. Pressure, Volume and Temperature are path independent State variables and Heat transferred and Work done are Path dependent variables. Definitions of Isobaric, Isochoric, Isothermal and Adiabatic processes. Does the heat transferred to a system always go in increasing its Internal Energy ?
Two graphs shown in the figure are the two Isotherms at their respective temperatures. Is T1 > T2 or T2 > T1 ?
Relation between Work Done on a system and change in its Internal Energy.
A container of volume 1 m3 is divided into two equal compartments by a partition. One compartment has a mixture of gases ( g = 1.5 ) 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.
Work done BY the gas for Isobaric, Isochoric and Isothermal processes.
First Law of Thermodynamics relates the Heat Transferred to a system, Change in its Internal Energy and Work Done BY the system. CHANGE ICON
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
Application of First Law of Thermodynamics for Isochoric, Isobaric and Isothermal processes. Equation of Internal Energy in terms of Molar Heat Capacity at constant Volume and Molar Heat Capacity at constant Pressure.
Two moles of an ideal gas at a temperature To = 300 K were cooled isochorically so that the gas pressure reduced h = 2 times. 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?
Derivation of Equation for an Adiabatic process.
For an ideal gas
a) the change in internal energy at the constant pressure when the temperature
of n mole of the gas change by DT is n Cv DT.
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 ( g = Cp / Cv )
Definition of Polytropic process and derivation of expression of Work Done, Internal Energy and Heat transfer in a Polytropic process.
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
Molar Heat Capacity of an Ideal gas is not the same and depends on the Thermodynamic process. Calculating the Molar Heat Capacity for Isobaric, Isochoric, Isothermal, Adiabatic and Polytropic process. And derivation of general equation of Molar Heat Capacity of an ideal gas.
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
70 calories of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30o C to 35o C. The amount of the heat ( in calories ) required to raise the temperature of the same gas through the same range ( 30o C to 35o C ) at constant volume is
Cyclic Thermodynamic process is one where the initial and final state of system is same. Relation between the Work done and Heat Transfer in a cyclic process.
Figure shows the P-V diagram for a fixed mass of an ideal gas undergoing cyclic process. AB represents isothermal process and CA represents adiabatic process. Which of the graphs shown in the following figure represents the P-T diagram of the cyclic process?
The following figure shows a cyclic process ABCA on a V-T diagram.
An ideal monoatomic gas is taken around the cycle ABCDA as shown in the P - V diagram.
The figure shows the 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,
(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
What gives direction to time ? Definition of Entropy and Second Law of Thermodynamics
A quantity of heat DH 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 at 27 oC. During the compression, 600 J of work is done on the gas. Find the entropy change of the gas.
Definition of Heat Engines. Is it possible to convert Work completely into Heat ? Is it possible to convert Heat completely into Work ? Discussion on Carnot Engine.
Efficiency of Carnot Engine.
Let the temperature Tsource and Tsink of the two heat reservoirs in the ideal Carnot engine be 1500 K and 500 K respectively. Which of these, increasing Tsource by 100 K or decreasing Tsink by 100 K, would result in a greater improvement in the efficiency of the engine?
An ideal gas is taken through a cyclic thermodynamic process involving four step. The amounts of heat involved in these step are Q1 = 5960 J, Q2 = - 5585 J, Q3 = - 2980 J and Q4 = 3645 J respectively. The corresponding amount of work done are W1 = 2200 J, W2 = - 825 J and W3 = - 1100 J and W4 respectively. The efficiency of the cycle is h. Then
Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. 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 30 K, then the rise in temperature of the gas in B is
(a) 30 K
(b) 18 K
(c) 50 K
(d) 42 K
P-V plots for two gases during adiabatic processes are shown in the figure. Plots 1 and 2 should corresponds respectively to (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 5 J, the work done by the gas in the process A - B is
(a) - 5 J
(b) - 10 J
(c) - 15 J
(d) - 20 J
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. If f is the number of degrees of freedom of gas molecules and W is the work done by the gas during the expansion, then
Two moles of a monoatomic ideal gas occupy a volume V at 27 oC. The gas is expanded adiabatically to a volume 2 root 2 V. Gas constant R = 8.3 J K-1 mol-1
i) The final temperature of the gas is
ii) The change in the internal energy of the gas in this process is
iii) The work done by the gas during the process is
One mole of an ideal mono atomic gas is taken round the cyclic process ABCA as shown in the figure.
i) The work done by the gas is
ii) The heat energy rejected by the gas in the process A - B is
iii) The heat energy rejected by the gas in the process C - A is
iv) The heat energy rejected by the gas in the process B - C is
Two moles of an ideal gas with volume V, pressure 2P and temperature T undergo a cyclic process ABCDA as shown in the figure
Two moles of an ideal monoatomic gas is taken through a cycle ABCA as shown in the P - T diagram. During the process AB, pressure and temperature of the gas vary such that PT = K, where K is a constant.
A sample of 2 kg of monoatomic helium ( assumed ideal ) is taken through the process ABC and another sample of 2 kg of the same gas is taken through the process ADC as shown in the figure. The molecular mass = 4 and R = 8.3 J K-1 mol-1.
Two moles of an ideal monoatomic 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.
Two different adiabatic paths for the same gas intersect two isothermals at T1 and T2 as shown in P - V diagram. How does VD / VA compare by VC / VB ?
Two moles of helium gas ( = 5/3) are initially at temperature 27 oC and occupy a volume of 20 liters. 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 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 monoatomic ideal gas is taken through a cyclic process starting from A as shown in the figure. Given VB/VA = 2 and VD/VA = 4. The temperature TA = 27 oC. R is the gas constant.
One mole of a diatomic ideal gas (g = 1.4) 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, process C ? D is an adiabatic expansion and process D ? A is isochoric. The volume ratios are = 16 and = 2 and the temperature at A is TA = 300 K. 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
Find P - V diagram, P - T diagram,
net work done and net heat supplied
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 is mA and that in B is mB. 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 DP and 1.5 DP respectively. then
a) 4 mA = 9 mB
b) 2 mA = 3 mB
c) 3 mA = 2 mB
d) 9 mA = 4 mB
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
(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 form 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 g = 1.5.
A small spherical monoatomic ideal gas bubble is
trapped inside a liquid of density rl. 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).
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 ( = 5/3) 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.
(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 Q = 80 kJ, 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 = a V, where a is a constant. If the final volume of the gas is h 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 g.
One mole of an ideal gas having adiabatic exponent g 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 h 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 + a V, where T0 and a are constants. Assuming the moler heat capacity of the gas at constant pressure to be Cp, find moler the 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 = a/2 where a is a constant.
Find the work performed by one mole of this gas during its heating from temperature To to a temperature h times higher, and the equation of the process in the variables P, V.
The pressure in a monatomic gas increases linearly from 4 105 Nm-2 to 8 105 Nm-2 when its volume increases from 0.2 m3 to 0.5 m3. 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 with g = 5/3 and another gas B with g = 7/5 at a certain temperature T. The gram molecular weights of the gases A and B are 4 and 32 respectively. 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 gaseoue mixture at T = 300 K.
c) If T is raised by 1 K from 300 K, find the percentage change un 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. Find the efficiency of this cycle if the volume of the ideal gas changes a = 10 times within the cycle. Take the working substance to be nitrogen.
A cycle consists of two isobaric and two adiabatic lines. Assuming the working substance to be an ideal gas with adiabatic exponent g, find the efficiency of the cycle if the pressure changes n times within the cycle.