EASY

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The pressure and volume of an ideal gas are related as $P V^{\frac{3}{2}} = K$ (Constant). The work done when the gas is taken from state $A (P_{1}, V_{1}, T_{1})$ to state $B (P_{2}, V_{2}, T_{2})$ is :

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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.

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

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

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

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)

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

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

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

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>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

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:

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

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)

MEDIUM

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

Match the thermodynamics processes taking place in a system with the correct conditions. In the table : $∆ Q$ is the heat supplied, $∆ W$ is the work done and $∆ U$ is change in internal energy of the system.

	Process		Condition
(I)	Adiabatic	(A)	$∆ W = 0$
(II)	Isothermal	(B)	$∆ Q = 0$
(III)	Isochoric	(C)	$∆ U \neq 0, ∆ W \neq 0, ∆ Q \neq 0$
(IV)	Isobaric	(D)	$∆ U = 0$

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

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) :

The pressure and volume of an ideal gas are related as PV32=K (Constant). The work done when the gas is taken from state AP1, V1, T1 to state BP2, V2, T2 is :

Important Questions on Thermodynamics

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The pressure and volume of an ideal gas are related as $P V^{\frac{3}{2}} = K$ (Constant). The work done when the gas is taken from state $A (P_{1}, V_{1}, T_{1})$ to state $B (P_{2}, V_{2}, T_{2})$ is :