One mole of a monoatomic gas behaving as per PVnRT at 27C is subjected to reversible isoentropic compression untill final temperature reaches 327C If the initial pressure was 10atm then the value of lnP final is given ln207

EASY

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:

MEDIUM

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

When

5

moles of

He

gas expand isothermally and reversibly at

300 K

from

10

litres to

20

litres, the magnitude of the maximum work obtained in

J

is . [nearest integer ] (Given :

R = 8.3 J K^{- 1} {mol}^{- 1}

and

\log 2 = 0.3010

)

HARD

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume

u = \frac{U}{V} \propto T^{4}

and pressure

p = \frac{1}{3} (\frac{U}{V})

. If the shell now undergoes an adiabatic expansion the relation between T and R is:

MEDIUM

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

The bulk modulus of a gas is defined as,

B = \frac{- V d P}{d V}

. For an adiabatic process, the variation of

B

is proportional to

P^{n}

. For an ideal gas,

n

is

EASY

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

Write features of reversible process.

HARD

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

The heat capacity of one mole an ideal is found to be

C_{V} = \frac{3 R (1 + a R T)}{2}

where

a

is constant. The equation obeyed by this gas during a reversible adiabatic expansion is:

HARD

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

One mole of an ideal monoatomic gas undergoes two reversible processes $(A \to B$ and $B \to C)$ as shown in the given figure:

Question Image

$A \to B$ is an adiabatic process. If the total heat absorbed in the entire process $(A \to B$ and $B \to C)$ is ${RT}_{2} \ln 10$ , the value of $2 {logV}_{3}$ is
[Use molar heat capacity of the gas at constant pressure, $C_{p, m} = \frac{5}{2} R$ ]

HARD

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

A mixture of ideal gas containing

5

moles of monatomic gas and

1

mole of rigid diatomic gas is initially at pressure

P_{0},

volume

V_{0}

and temperature

T_{0} .

If the gas mixture is adiabatically compressed to a volume

\frac{V_{0}}{4}

, then the correct statement(s) is/are,
(Given

2^{1.2} = 2.3; 2^{3.2} = 9.2; R

is gas constant)

EASY

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

Define:
Reversible process

HARD

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

Three separate reversible processes

(1, 2 and 3)

are carried out with

1

mole of an ideal gas initially at STP. In these processes, the pressure (

P

) is measured while increasing any one of the quantities volume (

V

), temperature (

T

) and number of moles

(n)

, keeping the other two constant. Plots of

P (atm)

versus

X

are found to be linear, where

X = n

or

T (K)

or

1 / V ({lit}^{- 1})

. For the processes

1, 2

and

3

, the numerical values of the slopes

m_{1}, m_{2}

and

m_{3}

of the

P

versus

X

plots are found to follow the order

m_{1} > m_{2} > m_{3}

, respectively. The correct statement(s) about these processes is/are

MEDIUM

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

Two moles of an ideal monoatomic gas occupies a volume $V$ at $27^{o} C$ . The gas expands adiabatically to a volume $2 V$ . Calculate $(a)$ the final temperature of the gas and $(b)$ change in its internal energy.

MEDIUM

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

During a reversible adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio

\frac{C_{p}}{C_{V}}

for the gas is

HARD

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P-V diagrams in column 3 of the table. Consider only the path from state

1

to state

2

.

W

denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic process. Here

γ

is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is

n

.

Column – 1	Column – 2	Column – 3
(I) $W_{1 \to 2} = \frac{1}{γ - 1} (P_{2} V_{2} - P_{1} V_{1})$	(i) Isothermal	(P)
(II) $W_{1 \to 2} = - P V_{2} + P V_{1}$	(ii) Isochoric	(Q)
(III) $W_{1 \to 2} = 0$	(iii) Isobaric	(R)
(IV) $W_{1 \to 2} = - n R T \ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic	(S)

Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in ideal gas?

MEDIUM

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

One mole of an ideal monatomic gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is

100 K

and the universal gas constant

R = 8.0 J mo l^{- 1} K^{- 1}

, then how much is the decrease in its internal energy (in

J

) ?

HARD

Physical Sciences>Matter and Its Interactions>Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.>Structure and Properties of Matter - Gases and liquids are made of molecules or inert atoms that are moving about relative to each other

An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P-V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic process. Here

γ

is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is

n

.

Column – 1	Column – 2	Column – 3
(I) $W_{1 \to 2} = \frac{1}{γ - 1} (P_{2} V_{2} - P_{1} V_{1})$	(i) Isothermal	(P)
(II) $W_{1 \to 2} = - P V_{2} + P V_{1}$	(ii) Isochoric	(Q)
(III) $W_{1 \to 2} = 0$	(iii) Isobaric	(R)
(IV) $W_{1 \to 2} = - n R T \ln (\frac{V_{2}}{V_{1}})$	(iv) Adiabatic	(S)

Which one of the following options is the correct combination?