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Two moles of an ideal gas have undergone a cyclic process $1 - 2 - 3 - 1$ . If net heat exchange in the process is $- 300 J$ , then work done by the gas in the process $2 - 3$ is $(R = 8.3 J m o l^{- 1} K^{- 1})$

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Important Questions on Thermodynamics

HARD

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by

P V^{n} =

constant, then n is given by (Here

C_{P}

and

C_{V}

are molar specific heat at constant pressure and constant volume, respectively) :

HARD

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

The equation of state of $n$ moles of a non-ideal gas can be approximated by the equation $(p + \frac{n^{2} a}{V^{2}}) (V - n b) = n R T$ where, $a$ and, $b$ are constant characteristics of the gas. Which of the following can represent the equation of a quasi-static adiabatic for this gas (assume that, $C_{V}$ is the molar heat capacity at constant volume is independent of temperature)?

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

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.

HARD

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

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 of the following options is the only correct representation of the process

∆ U = ∆ Q - P ∆ V

HARD

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

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>Thermodynamics>First Law of Thermodynamics

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

EASY

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

One mole of a monoatomic ideal gas expanded by a process described by

P V^{3} = C

where

C

is a constant. The heat capacity of the gas during the process is given by (

R

is the gas constant)

HARD

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

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)

HARD

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

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

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

One mole of an ideal monatomic gas undergoes a process described by the equation

P V^{3} =

constant. The heat capacity of the gas during this process is

EASY

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

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>Thermodynamics>First Law of Thermodynamics

A gas obeying the equation of state

P V = R T

undergoes a hypothetical reversible process described by the equation,

P V^{\frac{5}{3}} \exp (- \frac{P V}{E_{0}}) = C_{1}

, where

C_{1}

and

E_{0}

are dimensioned constants. Then, for this process, the thermal compressibility at high temperature

EASY

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

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:

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

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

) ?

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

A sample of an ideal gas is taken through the cyclic process

a b c a

as shown in the figure. The change in the internal energy of the gas along the path

c a

- 180 J .

The gas absorbs

250 J

of heat along the path

a b

and

60 J

along the path

b c

. The work done by the gas along the path

a b c

is:

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

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>Thermodynamics>First Law of Thermodynamics

Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? Where,

1 \to 2

is adiabatic. (Graphs are schematic and are not to scale)
Question Image

EASY

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

A gas at initial temperature

T

undergoes sudden expansion from volume

V

2 V .

Then.

EASY

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

Figure below shows two paths that may be taken by a gas to go from a state A to a state C.
Question Image

In process AB,

400 J

of heat is added to the system and in process BC,

100 J

of heat is added to the system. The heat absorbed by the system in the process AC will be:

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>First Law of Thermodynamics

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) :

Two moles of an ideal gas have undergone a cyclic process 1 – 2 – 3 – 1 . If net heat exchange in the process is -300 J , then work done by the gas in the process 2-3 is R=8.3 J mol-1 K-1

Important Questions on Thermodynamics

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Two moles of an ideal gas have undergone a cyclic process $1 - 2 - 3 - 1$ . If net heat exchange in the process is $- 300 J$ , then work done by the gas in the process $2 - 3$ is $(R = 8.3 J m o l^{- 1} K^{- 1})$