Thermodynamic Processes

We consider a thermodynamic system. If $\Delta U$ is the increase in internal energy and $W$ is the work done by the system, which one of the following statement is true?

Out of the following relations which one is true in the case of an adiabatic process, where $\gamma = C_p/C_v$?

The thermodynamic process in which no work is done by the gas or on the gas is

When the temperature of 4 moles of a gas was increased from $70^\circ$C to $90^\circ$C, at constant volume, the change in internal energy was $60$ J. The total heat capacity of the gas at constant volume is

In thermodynamic isobaric process

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $\Delta Q : \Delta U : \Delta W$ is ______.

If a gas is compressed isothermally then the r.m.s. velocity of the molecules

A thermodynamic system is compressed adiabatically, then its temperature

In an adiabatic expansion, the temperature of one mole of an ideal monatomic gas ( $\gamma = 5/3$) decreases from 60 K to 50 K. The work done by the gas in the process is:

(Take the universal gas constant as $R = 8.3\text{ J mol}^{-1}\text{ K}^{-1}$)

In an adiabatic process, which one of the following statement is true?

Consider the following statements:

A. Zeroth law of thermodynamics gives concept of temperature

B. First law of thermodynamics gives concept of internal energy

C. In isothermal expansion of ideal gas, $\Delta Q \neq \Delta W$

D. Product of intensive and extensive variables is extensive

E. The ratio of any extensive variable to mass will be an extensive variable

Choose the correct combination of statements from the options given below:

A vessel contains 0.15 m3 of a gas at pressure 8 bar and temperature 140 °C with $c_p = 3R$ and $c_v = 2R$. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is _________ kJ. (R is gas constant)

A diatomic gas $(\gamma = 1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the gas ______ J.

Heat is supplied to a rigid diatomic gas at constant pressure. The ratio of $\Delta Q : \Delta U : \Delta W$ is $\{\Delta Q =$ heat supplied$, \Delta U =$ change in internal energy $, \Delta W =$ work done during expansion$\}$

Two moles of a rigid diatomic gas does a work $\frac{Q}{4}$ when the amount of heat supplied is $Q$. In this process the total heat capacity of the gas is ($R$ = gas constant)

How much heat energy in joule must be supplied to $14$ g of nitrogen at room temperature to raise its temperature by $40^\circ$C at constant pressure?

(molecular wt. of nitrogen = $28$ g, $R$ = gas constant) (gas is diatomic)

If the ratio of molar heat capacities $\frac{C_p}{C_v} = \gamma$ then the ratio of $\frac{\Delta Q}{\Delta U}$ and $\frac{\Delta Q}{\Delta W}$ in an isobaric process is

Heat required to raise the temperature of 2 mol of an ideal gas at constant pressure from $25^\circ$C to $35^\circ$ C is 310 J. The amount of heat required to raise the temperature of the gas through the same range at constant volume is

($R = 8.3$ J/mol K)

Six moles of oxygen gas is heated from $20^\circ$C to $35^\circ$C at constant volume. If specific heat capacity at constant pressure is $8$ cal mol$^{-1}$k $^{-1}$ and gas constant is $2$ cal mol$^{-1}$k $^{-1}$. The change in internal energy of the gas is

The r.m.s. speed of hydrogen at S.T.P. is '$u$' m/s. If the gas is heated at constant pressure till its volume becomes three times, the final temperature of the gas and the r.m.s. speed are respectively

Two cylinders A and B fitted with pistons contain equal amount of an ideal diatomic gas at 303 K. The piston of cylinder A is free to move and that of cylinder 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 cylinder B is 63 K then the rise in temperature of the gas in A is

The heat energy that must be supplied to 14 g of nitrogen at room temperature to raise its temperature by $48^\circ$C at constant pressure is ($R$ = gas constant, Molecular weight of nitrogen $(\text{N}_2)$ = 28)

The change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure P is ($\gamma$ is the ratio of specific heat at constant pressure to that of volume) ($\gamma = \frac{C_p}{C_v}$)

If $\Delta Q$ is the amount of heat supplied to 'n' moles of a rigid diatomic gas at constant pressure, $\Delta U$ is the change in internal energy and $\Delta W$ is the work done then $\Delta W : \Delta U : \Delta Q$ is

5 moles of unknown gas is heated at constant volume from 10°C to 20°C. The molar specific heat of this gas at constant pressure $c_p = 8$ cal/mol.°C and $R = 8.36$ J/mol.°C. The change in the internal energy of the gas is __________ calorie.

10 mole of oxygen is heated at constant volume from $30^\circ\text{C}$ to $40^\circ\text{C}$. The change in the internal energy of the gas is ______ cal. (The molecular specific heat of oxygen at constant pressure, $C_P = 7\text{ cal/mol.}\,{}^\circ\text{C}$ and $R = 2\text{ cal./mol.}\,{}^\circ\text{C.})$

Two identical containers A and B with friction-less pistons contain the same ideal gas at the same temperature and the same volume, $V$. The mass of gas in A is $m_A$ and that in B is $m_B$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2V$. The changes in pressure in A and B are found to be $\Delta p$ and $3\Delta p$ respectively. Then

The temperature of an ideal gas increases $2$ times when compressed adiabatically to half the volume. Its equation of state is

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio $C_p/C_v$ for the gas is

A rigid diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\left(\frac{V_i}{32}\right)$, where $V_i$ is the initial volume. The initial temperature of the gas is '$T_i$ ' K and the final temperature is '$xT_i$ ' K. The value of $x$ is

An ideal gas ($\gamma = 1.5$) is expanded adiabatically. To reduce the root mean square velocity of molecules two times, the gas should be expanded

A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $\gamma = 1.5$, then the increase in the temperature of the gas in Kelvin is ($\gamma$ is the ratio of specific heats)

An ideal gas at $27^\circ$C is compressed adiabatically to $\left(\frac{8}{27}\right)$ of its original volume. If $\gamma = 5/3$, then the rise in temperature of a gas is

An ideal gas is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. speed of molecules 3 times? ($\gamma = 1.5$)

A monoatomic gas is stored in a thermally insulated container and the gas is suddenly compressed to $\left(\frac{1}{8}\right)^{th}$ of its initial volume. The ratio of final pressure to initial pressure is

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given, $\gamma = \frac{3}{2}$ ):

An ideal gas expands adiabatically ($\gamma = 1.5$). To reduce the r.m.s. velocity of the molecules 3 times the gas has to be expanded

Initial pressure and volume of a monoatomic ideal gas are $P$ and $V$. The change in internal energy of this gas in adiabatic expansion to volume $V$final $= 27\,V$ is ______ J.

The volume of an ideal gas increases 8 times and temperature becomes $(1/4)$th of initial temperature during a reversible change. If there is no exchange of heat in this process $(\Delta Q = 0)$ then identify the gas from the following options (Assuming the gases given in the options are ideal gases):

An ideal gas having pressure $P$, volume $V$ and temperature $T$ is expanded isothermally, to a volume $3V$ and final pressure $P_I$. The same gas is expanded adiabatically to a volume $3V$, the final pressure being $P_A$. The ratio $\frac{P_A}{P_I}$ is $\left(\frac{C_P}{C_V} = \gamma\right)$

An ideal gas with pressure P, volume V and temperature T is expanded isothermally to volume 2V and a final pressure $P_i$. The same gas is expanded adiabatically to a volume 2V then the final pressure is $P_a$. In terms of $\gamma$, the ratio of the two specific heats for the gas, the ratio $P_i/P_a$ is

Two samples A and B of gas initially at the same pressure and temperature. They are compressed from volume $V$ to $\frac{V}{2}$ (A isothermally and B adiabatically). The relation between pressure of the gas A ($P_A$) and pressure of gas B ($P_B$) is

One mole of an ideal diatomic gas expands from volume $V$ to $2V$ isothermally at a temperature $27^\circ\text{C}$ and does $W$ joule of work. If the gas undergoes same magnitude of expansion adiabatically from $27^\circ\text{C}$ doing the same amount of work $W$, then its final temperature will be (close to) $\underline{\hspace{3em}}\ ^\circ\text{C}.\ (\log_e 2 = 0.693)$

A monoatomic gas undergoes adiabatic change. Its pressure $P$ and temperature $T$ are related as $P \propto T^{x}$ where $x$ is

An ideal rigid diatomic gas $\left(\gamma = \frac{7}{5}\right)$ undergoes an adiabatic change. If the relation between temperature and volume is $TV^{x} =$ constant then the value of x is

A rigid diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as $P \propto T^{x}$ where x is

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is $4\text{ cm}^{2}$. The gas is heated slowly to raise the temperature by $1.2^\circ\text{C}$ during which the piston moves by 25 mm. The amount of heat supplied to the gas is ______ J. (Atmospheric pressure $= 100\text{ kPa}, R = 8.3\text{ J/mol.K}$) (Neglect mass of the piston)

The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of $17\text{ cm}^{2}$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by $4^\circ\text{C}$, then the piston will move ______ cm.

(atmospheric pressure $= 10^{5}\text{ Pa}$)

A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ be the lengths of the gas column before and after expansion respectively, then $\frac{T_1}{T_2}$ is

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P, V, T$. Heating is started from left side until pressure changes to $27P/8$. If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is ______ litres. (for this ideal gas $C_P/C_V = 1.5$)

A monoatomic gas at pressure P having volume V expands isothermally to a volume 3V and then adiabatically to a volume 81 V. The final pressure of the gas is ($\gamma = 5/3$).

An ideal gas undergoes a process maintaining relation between pressure $(P)$ and $\text{volume}(V)$ as ${}$

$P = P_0\left(1 + \left(\frac{V_0}{V}\right)^{2}\right)^{-1}$, where $P_0$ and $V_0$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_0$ and $3V_0$ respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, $T_B - T_A$ is ______. ( $R =$ gas constant)

In the thermodynamic processes, which of the following statements is NOT true?

Heat supplied $dQ =$ increase in internal energy dU is true for

During thermodynamic process, the increase in internal energy of a system is equal to the $\text{work}$ done on the system. Which process does the system undergo?

Match List - I with List - II.

Choose the correct answer from the options given below:

Identify the characteristics of an adiabatic process in a monoatomic gas.

(A) Internal energy is constant.

(B) Work done in the process is equal to the change in internal energy.

(C) The product of temperature and volume is a constant.

(D) The product of pressure and volume is a constant.

(E) The work done to change the temperature from $T_1$ to $T_2$ is proportional to $(T_2 - T_1)$. Choose the correct answer from the options given below:

Match the List - I with List - II

Choose the correct answer from the options given below:

Heat is given to an ideal gas in an isothermal process. Then

A. internal energy of the gas will decrease.

B. internal energy of the gas will increase.

C. internal energy of the gas will not change.

D. the gas will do negative work.

If a gas is compressed isothermally then the r.m.s. velocity of its molecules

When the heat is given to a gas in an Isothermal process, then there will be

During the isothermal expansion, a confined ideal gas does $(-150)\text{ J}$ of work against its surroundings. This means that

The work done in an adiabatic change in an ideal gas depends upon only:

In an adiabatic process, which of the following statements is true?

Match List - I with List - II.

$\Delta Q =$ Heat supplied

$\Delta W =$ Work done by the system

$\Delta U =$ Change in internal energy

$P =$ Pressure of the system

$\Delta V =$ Change in volume of the system

Choose the correct answer from the options given below:

An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to 4 times of its initial volume $(V_0)$, then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason (R): In isothermal process, PV = constant, while in adiabatic process $PV^{\gamma}$ = constant. Here $\gamma$ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas. In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.

Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below:

Two cylinders A and B fitted with piston contain equal amount of an ideal diatomic gas at temperature T K. The piston of cylinder A is free to move while that of cylinder $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise of temperature of the gas in A is $dT_A$, then the rise in temperature of the gas in B is $\left(\gamma = \frac{C_p}{C_v}\right)$

The heat energy that must be supplied to 14 gram of nitrogen at room temperature to raise its temperature by $48^\circ\text{C}$ at constant pressure is (Molecular weight of nitrogen $= 28, R =$ gas constant, $C_p = \frac{7}{2}R$ for diatomic gas)

A sample of an ideal gas $\left(\gamma = \frac{5}{3}\right)$ is heated at constant pressure. If 100 J of heat is supplied to the gas, the work done by the gas is

In an isobaric process of an ideal gas, the ratio of heat supplied and work done by the system $\left(\frac{Q}{W}\right)$ is $\left[\frac{C_P}{C_V} = \gamma\right]$.

When an ideal gas $\left(\gamma = \frac{5}{3}\right)$ is heated under constant pressure, then what percentage of given heat energy will be utilised in doing external work?

Two cylinders A and B fitted with pistons contain equal amount of an ideal rigid diatomic gas at 303 K. The piston of cylinder $A$ is free to move and that of cylinder B is held fixed. The same amount heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder B is 49 K, then the rise in temperature of the gas in $A$ is

The change in the internal energy of the mass of gas, when the volume changes from V to 2 V at constant pressure P is $\left(\gamma = \frac{C_p}{C_v}\right)$

A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in increasing the internal energy and that used for doing external work is $A$ and $B$ respectively. Then the ratio, $A : B$ is

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature.

A. The work done by gas during the process is zero.

B. The heat added to gas is different from change in its internal energy.

C. The volume of the gas is increased.

D. The internal energy of the gas is increased.

E. The process is isochoric (constant volume process)

Choose the correct answer from the options given below:

The temperature of 1 mole of an ideal monoatomic gas is increased by $50^\circ\text{C}$ at constant pressure. The total heat added and change in internal energy are $E_1$ and $E_2$, respectively. If $\frac{E_1}{E_2} = \frac{x}{9}$ then the value of $x$ is _________.

A gas having $\gamma = \frac{5}{2}$ and volume 360 c.c. is suddenly compressed to 90 c.c. If the initial pressure of the gas is P, then the final pressure will be

An ideal gas expands adiabatically, $(\gamma = 1.5)$. To reduce the r.m.s. velocity of the molecules 4 times, the gas has to be expanded

A monoatomic ideal gas is compressed adiabatically to $\left(\frac{1}{27}\right)$ of its initial volume. If initial temperature of the gas is ' T ' K and final temperature is ' xT ' K, the value of ' x ' is

A polyatomic gas is compressed to $\left(\frac{1}{8}\right)$th of its volume adiabatically. If its initial pressure is $P_0$, its new pressure will be [Given, $\frac{C_p}{C_v} = \frac{4}{3}$ ]

A diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_0}{32}$, where $V_0$ is its initial volume. The initial temperature of the gas is $T_i$ in kelvin and the final temperature is $xT_i$ in kelvin. The value of $x$ is

A monoatomic gas having $\gamma = \frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to $\left(\frac{1}{8}\right)$th of its initial volume. The ratio of final pressure and initial pressure is: ($\gamma$ is the ratio of specific heats of the gas at constant pressure and at constant volume)

An ideal gas initially at $0^\circ\text{C}$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3/2$, the change in temperature due to the thermodynamic process is _________ K.

When a diatomic gas (rigid) undergoes adiabatic change, its pressure $(P)$ and temperature $(T)$ are related as $P \propto T^{c}$. The value of $c$ is

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800\text{ cm}^{3}$ and temperature $27^\circ\text{C}$. The change in temperature when the gas is adiabatically compressed to $200\text{ cm}^{3}$ is:

(Take $\gamma = 1.5; \gamma$ is the ratio of specific heats at constant pressure and at constant volume)

Three samples $X, Y$, and $Z$ of same gas have equal volumes and temperatures. The volume of each sample is doubled, the process being isothermal for X, adiabatic for Y and isobaric for Z. If the final pressures are equal for the three samples, the ratio of the initial pressures is ( $\gamma = 3/2$)

Two gases $A$ and $B$ are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas $A$ and $B$ are displaced by 16 cm and 9 cm, respectively. If the change in their internal energy is the same, then the ratio $\frac{r_A}{r_B}$ is equal to

A piston of mass $M$ is hung from a massless spring whose restoring force law goes as $F = -kx^{3}$, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' $n$ ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height $L_0$ to $L_1$, the total energy delivered by the filament is:(Assume spring to be in its natural length before heating)

A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature $T_2$. If $L_1$ and $L_2$ are the lengths of the gas columns before and after expansion respectively, then $(T_2/T_1)$ is given by

A polyatomic gas at pressure P, having volume ' $V$ ' expands isothermally to a volume ' 3 V ' and then adiabatically to a volume ' 24 V '. The final pressure of gas is (for moderate temperature changes)

A gas undergoes a change in which its pressure ' P ' and volume ' V ' are related as $PV^{n} =$ constant, where n is a constant. If the specific heat of the gas in this change is zero, then the value of $n$ is ( $\gamma =$ adiabatic ratio)