Thermodynamic processes are indicated in the following diagram. Match the following Column – 1 Column - 2 P. Process I a. Adiabatic Q. Process II b. Isobaric R. Process III c. Isochoric S. Process IV d. Isothermal

P → c , Q → a , R → d , S → b

P → a , Q → c , R → d , S → b

P → c , Q → d , R → b , S → a

P → d , Q → b , R → a , S → c

HARD

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Two moles of an ideal monatomic gas is taken through a cycle $A B C A$ as shown in the $p - T$ diagram. During the process $A B$ , the pressure and temperature of the gas vary such that $p T$ = constant. If $T_{1} = 300 K$ and the amount of heat released by the gas during the process $A B$ is $Q = - x R$ , then the value of $x$ is

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Important Questions on Thermodynamics

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

Thermodynamic processes are indicated in the following diagram.

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Match the following

Column – 1	Column - 2
P. Process I	a. Adiabatic
Q. Process II	b. Isobaric
R. Process III	c. Isochoric
S. Process IV	d. Isothermal

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

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

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

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

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

A monoatomic gas is compressed from a volume of

2 m^{3}

to a volume of

1 m^{3}

at a constant pressure of

100 N m^{2}

. Then it is heated at constant volume by supplying

150 J

of energy. As a result, the internal energy of the gas

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure,

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The change in internal energy of the gas during the transition is:

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

The three processes in a thermodynamic cycle shown in the figure are : Process $1 \to 2$ is isothermal; Process $2 \to 3$ is isochoric (volume remains constant); Process $1 \to 3$ is adiabatic.

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The total work done by the ideal gas in this cycle is, $10 J .$ The internal energy decreases by, $20 J$ in the isochoric process. The work done by the gas in the adiabatic process is, $- 20 J$ . The heat added to the system in the isothermal process is

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

An ideal gas has molecules with

5

degrees of freedom. The ratio of specific heats at constant pressure

(C_{p})

and at constant volume

(C_{V})

is:

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

In which of the following processes, heat is neither absorbed nor released by a system?

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

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:

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

For a rigid diatomic molecule, the universal gas constant

R = n C_{P}

, where,

C_{P}

is the molar specific heat at constant pressure and

n

is a number. Hence,

n

is equal to

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

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?

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

Half mole of an ideal monoatomic gas is heated at a constant pressure of

1 atm

from

20 ° C

90 ° C

. Work done by the gas is

(

Gas constant,

R = 8.21 J {mol}^{- 1} K^{- 1}

)

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

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?

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

In the $P - V$ diagram below the dashed curved line is an adiabatic

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For a process that is described by a straight line joining two points $X$ and $Y$ on the adiabatic (solid line in the diagram), heat is: (Hint: Consider the variations in temperature from $X$ and $Y$ along the straight line)

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non- expansion work is zero)

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

A diatomic gas with rigid molecules does

10 J

of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

Starting at temperature

300 K,

one mole of an ideal diatomic gas

(γ = 1.4)

is first compressed adiabatically from volume

V_{1}

V_{2} = \frac{V_{1}}{16} .

It is then allowed to expand isobarically to volume

2 V_{2}

. If all the processes are the quasi-static then the final temperature of the gas (in

K

) is (to the nearest integer) ___________.

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

An engine operates by taking

n

moles of an ideal gas through the cycle

A B C D A

shown in figure. The thermal efficiency of the engine is:

(Take

C_{v} = 1.5 R

, where

R

is gas constant)

Question Image

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

For the given cyclic process $C A B$ as shown for a gas, the work done is:

Question Image

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamic Processes and Indicator Diagrams

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:

Two moles of an ideal monatomic gas is taken through a cycle ABCA as shown in the p-T diagram. During the process AB, the pressure and temperature of the gas vary such that pT = constant. If T1=300 K and the amount of heat released by the gas during the process AB is Q=-xR, then the value of x is

Important Questions on Thermodynamics

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