Chapter 4

Which of the following is not a thermodynamic property of a system? (a) \(H\) (b) \(P\) (c) \(E\) (d) w

An average human produces about \(10 \mathrm{MJ}\) of heat each day through metabolic activity. If a human body were an isolated system of mass \(80 \mathrm{~kg}\) with the heat capacity of water, what temperature rise would the body experience? Heat capacity of water \(=4.2 \mathrm{~J} / \mathrm{K}-\mathrm{g} .\) (a) \(29.76^{\circ} \mathrm{C}\) (b) \(2.976 \mathrm{~K}\) (c) \(2.976 \times 10^{4 \circ} \mathrm{C}\) (d) \(0.029^{\circ} \mathrm{C}\)

The heat capacity of liquid water is \(75.6 \mathrm{~J} / \mathrm{K}-\mathrm{mol}\), while the enthalpy of fusion of ice is \(6.0 \mathrm{~kJ} / \mathrm{mol}\). What is the smallest number of ice cubes at \(0^{\circ} \mathrm{C}\), each containing \(9.0 \mathrm{~g}\) of water, needed to cool \(500 \mathrm{~g}\) of liquid water from \(20^{\circ} \mathrm{C}\) to \(0^{\circ} \mathrm{C}\) ? (a) 1 (b) 7 (c) 14 (d) 21

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume \(V_{1}\) and contains an ideal gas at pressure \(P_{1}\) and temperature \(T_{1}\). The other chamber has volume \(V_{2}\) and contains the same ideal gas at pressure \(P_{2}\) and temperature \(T_{2}\). If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be (a) \(\frac{T_{1} T_{2}\left(P_{1} V_{1}+P_{2} V_{2}\right)}{P_{1} V_{1} T_{2}+P_{2} V_{2} T_{1}}\) (b) \(\frac{P_{1} V_{1} T_{1}+P_{2} V_{2} T_{2}}{P_{1} V_{1}+P_{2} V_{2}}\) (c) \(\frac{P_{1} V_{1} T_{2}+P_{2} V_{2} T_{1}}{P_{1} V_{1}+P_{2} V_{2}}\) (d) \(\frac{T_{1} T_{2}\left(P_{1} V_{1}+P_{2} V_{2}\right)}{P_{1} V_{1} T_{1}+P_{2} V_{2} T_{2}}\)

The work involved \((w)\) in an isothermal expansion of \(n\) moles of an ideal gas from an initial pressure of ' \(P\) ' atm to final pressure of 1 atm in number of steps such that in every step the constant external pressure exactly 1 atm less than the initial pressure of gas is maintained, is given as (a) \(-n R T \sum_{i=1}^{i=P-1}\left(\frac{1}{P+1-i}\right)\) (b) \(-n R T \sum_{i=1}^{i=P}\left(\frac{1}{P+1-i}\right)\) (c) \(-n R T \sum_{i=1}^{i=P}\left(\frac{i}{P+1-i}\right)\) (d) \(-n R T \sum_{i=1}^{i=P-1}\left(\frac{i}{P+1-i}\right)\)

The internal energy change when a system goes from state \(A\) to \(B\) is \(40 \mathrm{~kJ} /\) mol If the system goes from \(A\) to \(B\) by a reversible path and returns to state \(\mathrm{A}\) by an irreversible path, what would be the net change in internal energy? (a) \(40 \mathrm{~kJ}\) (b) \(>40 \mathrm{~kJ}\) (c) \(\leq 40 \mathrm{~kJ}\) (d) Zero

A system is said to be in thermodynamic equilibrium with surrounding if (a) it is only in thermal equilibrium with surrounding. (b) it is in both thermal and chemical equilibrium with surrounding. (c) it is in thermal, chemical as well as mechanical equilibrium with the surrounding. (d) it is in thermal and mechanical equilibrium, but not in chemical equilibrium with surrounding.

If a closed system has adiabatic boundaries, then at least one boundary must be (a) permeable (b) imaginary (c) movable (d) fixed

Which of the following pair does show the extensive properties? (a) temperature and pressure (b) viscosity and surface tension (c) refractive index and specific heat (d) volume and heat capacity

Which of the following statement is correct? (a) Heat is thermodynamic property of system. (b) Work is thermodynamic property of system. (c) Work done by a conservative force is path function. (d) Heat involved in chemical reaction is path independent physical quantity.

The pressure and density of a diatomic gas \((\gamma=7 / 5)\) change from \(\left(P_{1}, d_{1}\right)\) to \(\left(P_{2},\right.\), \(d_{2}\) ) adiabatically. If \(d_{2} / d_{1}=32\), then what is the value of \(P_{2} / P_{1}\) ? (a) 32 (b) 64 (c) 128 (d) 256

For an isothermal process, the essential condition is (a) \(\Delta T=0\) (b) \(\Delta H=0\) (c) \(\Delta U=0\) (d) \(\mathrm{d} T=0\)

One mole of oxygen is heated from \(0^{\circ} \mathrm{C}\), at constant pressure, till its volume increased by \(10 \%\). The specific heat of oxygen, under these conditions, is \(0.22 \mathrm{cal} / \mathrm{g}-\mathrm{K}\). The amount of heat required is (a) \(32 \times 0.22 \times 27.3 \times 4.2 \mathrm{~J}\) (b) \(16 \times 0.22 \times 27.3 \times 4.2 \mathrm{~J}\) (c) \(\frac{32 \times 0.22 \times 27.3}{4.2} \mathrm{~J}\) (d) \(\frac{16 \times 0.22 \times 27.3}{4.2} \mathrm{~J}\)

A system absorbs \(20 \mathrm{~kJ}\) heat and does \(10 \mathrm{~kJ}\) of work. The internal energy of the system (a) increases by \(10 \mathrm{~kJ}\) (b) decreases by \(10 \mathrm{~kJ}\) (c) increases by \(30 \mathrm{~kJ}\) (d) decreases by \(30 \mathrm{~kJ}\)

The volume of a system becomes twice its original volume on the absorption of 300 cal of heat. The work done on the surrounding was found to be 200 cal. What is \(\Delta U\) for the system? (a) \(500 \mathrm{cal}\) (b) \(300 \mathrm{cal}\) (c) \(100 \mathrm{cal}\) (d) \(-500 \mathrm{cal}\)

With what minimum pressure must a given volume of an ideal gas \((\gamma=1.4)\), originally at \(400 \mathrm{~K}\) and \(100 \mathrm{kPa}\), be adiabatically compressed in order to raise its temperature up to \(700 \mathrm{~K}\) ? (a) \(708.9 \mathrm{kPa}\) (b) \(362.5 \mathrm{kPa}\) (c) \(1450 \mathrm{kPa}\) (d) \(437.4 \mathrm{kPa}\)

One mole of an ideal gas at \(300 \mathrm{~K}\) is expanded isothermally from an initial volume of \(1 \mathrm{~L}\) to \(10 \mathrm{~L}\). The change in internal energy, \(\Delta U\), for the gas in this process is (a) \(163.7 \mathrm{cal}\) (b) zero (c) \(1381.1 \mathrm{cal}\) (d) 9 L-atm

A container of volume \(1 \mathrm{~m}^{3}\) is divided into two equal parts by a partition. One part has an ideal diatomic gas at \(300 \mathrm{~K}\) and the other part has vacuum. The whole system is isolated from the surrounding. When the partition is removed, the gas expands to occupy the whole volume. Its temperature will be (a) \(300 \mathrm{~K}\) (b) \(227.5^{\circ} \mathrm{C}\) (c) \(455 \mathrm{~K}\) (d) \(455^{\circ} \mathrm{C}\)

Five moles of an ideal gas expand isothermally and reversibly from an initial pressure of \(100 \mathrm{~atm}\) to a final pressure of latm at \(27^{\circ} \mathrm{C}\). The work done by the gas is \((\ln 100=4.6)\) (a) \(2760 \mathrm{cal}\) (b) 6000 cal (c) 0 (d) \(13,800 \mathrm{cal}\)

If all degree of freedom of a three dimensional N-atomic gaseous molecule is excited, then \(C_{\mathrm{p}} / C_{\mathrm{v}}\) ratio of gas should be (a) \(1.33\) (b) \(1+\frac{1}{3 N-3}\) (c) \(1+\frac{1}{N}\) (d) \(1+\frac{1}{3 N-2}\)

The work done in the isothermal reversible expansion of argon gas at \(27^{\circ} \mathrm{C}\) from 41 to 161 was equal to 4200 cal. What is the amount of argon subjected to such an expansion? (Ar \(=40, \ln 4=1.4\) ) (a) \(5.0 \mathrm{~g}\) (b) \(20.0 \mathrm{~g}\) (c) \(200.0 \mathrm{~g}\) (d) \(48.1 \mathrm{~g}\)

The minimum work which must be done to compress \(16 \mathrm{~g}\) of oxygen isothermally, at \(300 \mathrm{~K}\) from a pressure of \(1.01325\) \(\times 10^{3} \mathrm{~N} / \mathrm{m}^{2}\) to \(1.01325 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\) is \((\ln 100=4.6, R=8.3 \mathrm{~J} / \mathrm{K}-\mathrm{mol})\) (a) \(5727 \mathrm{~J}\) (b) \(11.454 \mathrm{~kJ}\) (c) \(123.255 \mathrm{~kJ}\) (d) \(1232.55 \mathrm{~J}\)

For a reversible process at \(T=300 \mathrm{~K}\), volume of the ideal gas is increased from \(1 \mathrm{~L}\) to \(10 \mathrm{~L}\). If the process is isothermal, the \(\Delta H\) of the process is (a) \(11.47 \mathrm{~kJ}\) (b) \(4.98 \mathrm{~kJ}\) (c) 0 (d) \(-11.47 \mathrm{~kJ}\)

The magnitude of work done by one mole of a van der Waals gas, during its isothermal reversible expansion from volume \(V_{1}\) to \(V_{2}\) at temperature \(T \mathrm{~K}\), is (a) \(R T \ln \left(\frac{V_{2}}{V_{1}}\right)\) (b) \(R T \ln \left(\frac{V_{2}-b}{V_{1}-b}\right)\) (c) \(R T \ln \left(\frac{V_{2}-b}{V_{1}-b}\right)+a\left(\frac{1}{V_{2}}-\frac{1}{V_{1}}\right)\) (d) \(R T \ln \left(\frac{V_{2}-b}{V_{1}-b}\right)-a\left(\frac{1}{V_{2}}-\frac{1}{V_{1}}\right)\)

A sample of ideal gas is compressed from initial volume of \(2 V_{o}\) to \(V_{o}\) using three different processes (1) reversible isothermal (2) reversible adiabatic (3) irreversible adiabatic under a constant external pressure. Then (a) final temperature of gas will be highest at the end of \(2^{\text {nd }}\) process. (b) magnitude of enthalpy change of sample will be highest in isothermal process. (c) final temperature of gas will be highest at the end of \(3^{\text {rd }}\) process. (d) final pressure of gas will be highest at the end of second process.

The work done in an adiabatic change of fixed amount of an ideal gas depends on change in (a) volume (b) pressure (c) temperature (d) density

Inversion temperature is defined as the temperature above which a gas gets warm up and below which, the gas become cooler, when expanded adiabatically. Boyle temperature for a gas is \(20^{\circ} \mathrm{C}\). What will happen to the gas if it is adiabatically expanded at \(50^{\circ} \mathrm{C}\) ? (a) Heating (b) Cooling (c) Neither heating nor cooling (d) First cooling then heating

In the reversible adiabatic expansion of an ideal monoatomic gas, the final volume is 8 times the initial volume. The ratio of final temperature to initial temperature is (a) \(8: 1\) (b) \(1: 4\) (c) \(1: 2\) (d) \(4: 1\)

An adiabatic cylinder fitted with an adiabatic piston at the right end of cylinder, is divided into two equal halves with a monoatomic gas on left side and diatomic gas on right side, using an impermeable movable adiabatic wall. If the piston is pushed slowly to compress the diatomic gas to \(\frac{3}{4}\) th of its original volume. The ratio of new volume of monoatomic gas to its initial volume would be (a) \(\left(\frac{4}{3}\right)^{\frac{25}{21}}\) (b) \(\left(\frac{7}{5}\right)^{\frac{3}{4}}\) (c) \(\left(\frac{3}{4}\right)^{\frac{21}{25}}\) (d) \(\frac{3}{4}\)

Equal moles of \(\mathrm{He}, \mathrm{H}_{2}, \mathrm{CO}_{2}\) and \(\mathrm{SO}_{3}\) gases are expanded adiabatically and reversibly from the same initial state to the same final volume. The magnitude of work is maximum for (Assume ideal behaviour of gases and all the degree of freedoms are active.) (a) He (b) \(\mathrm{H}_{2}\) (c) \(\mathrm{CO}_{2}\) (d) \(\mathrm{SO}_{3}\)

One mole of a certain ideal gas is contained under a weightless piston of a vertical cylinder at a temperature \(T\). The space over the piston opens into the atmosphere. What work has to be performed in order to increase isothermally the gas volume under the piston \(n\) times by slowly raising the piston? The friction of the piston against the cylinder walls is negligibly small. (a) \(R T(n-1-\ln n)\) (b) \(R T(1-n+\ln n)\) (c) \(R T \ln n\) (d) \(-R T \ln n\)

Temperature of one mole of an ideal gas is increased by one degree at constant pressure. Work done by the gas is (a) \(R\) (b) \(2 R\) (c) \(R / 2\) (d) \(3 R\)

Two moles of an ideal gas \(\left[C_{\mathrm{v}, \mathrm{m}}\right.\) \(\left.\left(/ \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)=20+0.01 T(/ \mathrm{K})\right]\) is heated at constant pressure from \(27^{\circ} \mathrm{C}\) to \(127^{\circ} \mathrm{C}\). The amount of heat absorbed by the gas is (a) \(1662.8 \mathrm{~J}\) (b) \(4700 \mathrm{~J}\) (c) \(6362.8 \mathrm{~J}\) (d) \(3037.2 \mathrm{~J}\)

A portion of helium gas in a vertical cylindrical container is in thermodynamic equilibrium with the surroundings. The gas is confined by a movable heavy piston. The piston is slowly elevated by a distance \(H\) from its equilibrium position and then kept in the elevated position long enough for the thermodynamic equilibrium to be re-established. After that, the container is insulated and then the piston is released. After the piston comes to rest, what is the new equilibrium position of the piston with respect to initial position? (a) The piston ends up \(0.4 H\) above its initial position (b) The piston ends up \(0.6 H\) above its initial position (c) The piston ends at its initial position (d) The piston ends up \(0.4 H\) below its initial position

The maximum high temperature molar heat capacity at constant volume to be expected for acetylene which is a linear molecule is (a) 9 cal/deg-mole (b) \(12 \mathrm{cal} /\) deg-mole (c) \(19 \mathrm{cal} /\) deg-mole (d) \(14 \mathrm{cal} /\) deg-mole

Molar heat capacity of water in equilibrium with ice at constant pressure is (a) zero (b) infinity (c) \(40.45 \mathrm{~kJ} / \mathrm{K}\) -mol (d) \(75.48 \mathrm{~J} / \mathrm{K}-\mathrm{mol}\)

If one mole of a monoatomic gas \((\gamma=5 / 3)\) is mixed with one mole of a diatomic gas \((\gamma=7 / 5)\), the value of \(\gamma\) for the mixture is (a) 1 (b) \(1.5\) (c) 2 (d) \(3.0\)

The equation of state for one mole of a gas is \(P V=R T+B P\), where \(B\) is a constant, independent of temperature. The internal energy of fixed amount of gas is function of temperature only. If one mole of the above gas is isothermally expanded from \(12 \mathrm{~L}\) to \(22 \mathrm{~L}\) at a constant external pressure of 1 bar at \(400 \mathrm{~K}\), then the change in enthalpy of the gas is approximately \((\mathrm{B}=2 \mathrm{~L} / \mathrm{mol})\) (a) 0 (b) \(-3.32 \mathrm{~J}\) (c) \(-332 \mathrm{~J}\) (d) \(-166 \mathrm{~J}\)

When an ideal diatomic gas is a heated at a constant pressure, the fraction of heat energy supplied which increase the internal energy of the gas is (a) \(\frac{2}{5}\) (b) \(\frac{3}{5}\) (c) \(\frac{5}{7}\) (d) \(\frac{3}{7}\)

One mole of a real gas is subjected to heating at constant volume from \(\left(P_{1}\right.\), \(V_{1}, T_{1}\) ) state to \(\left(P_{2}, V_{1}, T_{2}\right)\) state. Then it is subjected to irreversible adiabatic compression against constant external pressure of \(P_{3}\) atm, till the system reaches final state \(\left(P_{3}, V_{2}, T_{3}\right) .\) If the constant volume molar heat capacity of real gas is \(C_{\mathrm{V}}\), then the correct expression for \(\Delta H\) from State 1 to State 3 is (a) \(C_{\mathrm{V}}\left(T_{3}-T_{1}\right)+\left(P_{3} V_{1}-P_{1} V_{1}\right)\) (b) \(C_{\mathrm{V}}\left(T_{2}-T_{1}\right)+\left(P_{3} V_{2}-P_{1} V_{1}\right)\) (c) \(C_{\mathrm{y}}\left(T_{2}-T_{1}\right)+\left(P_{3} V_{1}-P_{1} V_{1}\right)\) (d) \(C_{\mathrm{P}}\left(T_{2}-T_{1}\right)+\left(P_{3} V_{1}-P_{1} V_{1}\right)\)

An ideal gas \((\gamma=1.5)\) undergoes a change in state such that the magnitude of heat absorbed by the gas is equal to the magnitude of work done by the gas. The molar heat capacity of the gas in this process is (a) \(2 R\) (b) \(R\) (c) \(3 R\) (d) \(1.5 R\)

During an adiabatic process, the pressure of a gas is found to be proportional to cube of its absolute temperature. The Poisson's ratio of gas is (a) \(3 / 2\) (b) \(7 / 2\) (c) \(5 / 3\) (d) \(9 / 7\)

A diatomic ideal gas initially at \(273 \mathrm{~K}\) is given 100 cal heat due to which system did \(210 \mathrm{~J}\) work. Molar heat capacity of the gas for the process is \((1 \mathrm{cal}=4.2 \mathrm{~J})\) (a) \(\frac{3}{2} R\) (b) \(\frac{5}{2} R\) (c) \(\frac{5}{4} R\) (d) \(5 R\)

A reversible heat engine absorbs \(40 \mathrm{~kJ}\) of heat at \(500 \mathrm{~K}\) and performs \(10 \mathrm{~kJ}\) of work rejecting the remaining amount to the sink at \(300 \mathrm{~K}\). The entropy change for the universe is (a) \(-80 \mathrm{~J} / \mathrm{K}\) (b) \(100 \mathrm{~J} / \mathrm{K}\) (c) \(20 \mathrm{~J} / \mathrm{K}\) (d) \(180 \mathrm{~J} / \mathrm{K}\)

Molar heat capacity of \(\mathrm{CD}_{2} \mathrm{O}\) (deuterated form of formaldehyde) vapour at constant pressure is vapour 14 cal/K-mol. The entropy change associated with the cooling of \(3.2 \mathrm{~g}\) of \(\mathrm{CD}_{2} \mathrm{O}\) vapour from \(1000 \mathrm{~K}\) to \(900 \mathrm{~K}\) at constant pressure is (assume ideal gas behaviour for \(\mathrm{CD}_{2} \mathrm{O}\) ) \([\ln 0.9=-0.1]\) (a) \(+0.14 \mathrm{cal} / \mathrm{K}\) (b) \(-0.14 \mathrm{cal} / \mathrm{K}\) (c) \(-1.4 \mathrm{cal} / \mathrm{K}\) (d) \(+1.4 \mathrm{cal} / \mathrm{K}\)

2 moles of an ideal monoatomic gas undergoes reversible expansion from (4 \(\mathrm{L}\), \(400 \mathrm{~K}\) ) to \(8 \mathrm{~L}\) such that \(T V^{2}=\) constant. The change in enthalpy of the gas is (a) \(-1500 R\) (b) \(-3000 R\) (c) \(+1500 R\) (d) \(+3000 R\)

The change in entropy accompanying the heating of one mole of helium gas \(\left(C_{\mathrm{v} . \mathrm{m}}\right.\) \(=3 R / 2\) ), assumed ideal, from a temperature of \(250 \mathrm{~K}\) to a temperature of \(1000 \mathrm{~K}\) at constant pressure. \((\ln 2=0.7)\) (a) \(4.2 \mathrm{cal} / \mathrm{K}\) (b) \(7.0 \mathrm{cal} / \mathrm{K}\) (c) \(2.1 \mathrm{cal} / \mathrm{K}\) (d) \(3.5 \mathrm{cal} / \mathrm{K}\)

One mole of an ideal gas undergoes the following cyclic process: (i) Isochoric heating from \(\left(P_{1}, V_{1}, T_{1}\right)\) to double temperature. (ii) Isobaric expansion to double volume. (iii) Linear expansion (on \(P-V\) curve) to \(\left(P_{1}, 8 V_{1}\right) .\) (iv) Isobaric compression to initial state. If \(T_{1}=300 \mathrm{~K}\), the magnitude of net work done by the gas in the cyclic process is (a) \(2400 \mathrm{cal}\) (b) \(1200 \mathrm{cal}\) (c) \(4800 \mathrm{cal}\) (d) \(3600 \mathrm{cal}\)

A system undergoes a process in which the entropy change is \(+5.51 \mathrm{JK}^{-1}\). During the process, \(1.50 \mathrm{~kJ}\) of heat is added to the system at \(300 \mathrm{~K}\). The correct information regarding the process is (a) the process thermodynamically reversible. (b) the process is thermodynamically irreversible. (c) the process may or may not be thermodynamically reversible. (d) the process must be isobaric.

The latent heat of vaporization of a liquid at \(500 \mathrm{~K}\) and 1 atm pressure is \(10 \mathrm{kcal} / \mathrm{mol}\). What will be the change in internal energy if 3 moles of the liquid changes to vapour state at the same temperature and pressure? (a) \(27 \mathrm{kcal}\) (b) \(13 \mathrm{kcal}\) (c) \(-27 \mathrm{kcal}\) (d) \(-13\) kcal