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In isothermal compression, all work done on gas is transformed into-

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Important Questions on Heat and Thermodynamics

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

A gas at initial temperature

T

undergoes sudden expansion from volume

V

2 V .

Then.

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

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?

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

A spherical bubble inside water has radius

R

. Take the pressure inside the bubble and the water pressure to be

p_{0} .

The bubble now gets compressed radially in an adiabatic manner so that its radius becomes

(R - a)

. For

a ≪ R

the magnitude of the work done in the process is given by

(4 π P_{0} R a^{2}) X,

where

X

is a constant and

γ = C_{p} / C_{V} = 41 / 30

. The value of

X

is______

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where V is the volume and T is the temperature). Which of the statements below is (are) true?

Question Image

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

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)

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

An ideal gas is expanded from

(p_{1}, V_{1}, T_{1}) to (p_{2}, V_{2}, T_{2})

under different conditions. The correct statement(s) among the following is(are)

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

A thermodynamic cycle

x y z x

is shown on a

V

T

diagram.

The

P

V

diagram that best describes this cycle is: (Diagrams are schematic and not to scale)

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

An ideal gas goes through a reversible cycle

a \to b \to c \to d

has the V - T diagram shown below. Process

d \to a a n d b \to c

are adiabatic.

Question Image

The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

One mole of an ideal monatomic gas is taken along the path

A B C A

as shown in the

P - V

diagram. The maximum temperature attained by the gas along the path

B C

is given by:
Question Image

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is:

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure

P_{i} = 10^{5} Pa and volume V_{i} = 10^{- 3} m^{3}

changes to a final state at

P_{f} = (\frac{1}{32}) \times 10^{5} Pa and V_{f} = 8 \times 10^{- 3} m^{3}

in an adiabatic quasi-static process, such that

P^{3} V^{5} =

constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at

P_{i}

followed by an isochoric (isovolumetric) process at volumes

V_{f}

. The amount of heat supplied to the system in the two step process is approximately

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

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?

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

One mole of a monoatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature

(V - T)

diagram. The correct statement(s) is/are:

[

R

is the gas constant]
Question Image

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

n

moles of an ideal gas with constant volume heat capacity

C_{v}

undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is:

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

Consider one mole of helium gas enclosed in a container at initial pressure

P_{1}

and volume

V_{1}

. It expands isothermally to volume

4 V_{1}

. After this, the gas expands adiabatically and its volume becomes

32 V_{1}

. The work done by the gas during isothermal and adiabatic expansion processes are

W_{iso}

and

W_{a d i a},

\frac{W_{iso}}{W_{adia}} = f \ln (2)

, then

f

is _________ .

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecule changes from

τ_{1}

τ_{2}

. If

\frac{C_{P}}{C_{v}} = γ

for this gas then a good estimate for

\frac{τ_{2}}{τ_{1}}

is given by

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

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>Heat and Thermodynamics>Thermodynamic Processes

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

Question Image

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermodynamic Processes

A balloon filled with helium

(32 ° C and 1 .7 atm)

bursts. Immediately afterwards the expansion of helium can be considered as :

In isothermal compression, all work done on gas is transformed into-

Important Questions on Heat and Thermodynamics

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