Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are labelled as A → B , A → C and A → D . The change in internal energies during these process are taken as E A B , E A C and E A D and the work done as W A B , W A C and W A D . The correct relation between these parameters are:

E A B = E A C = E A D , W A B > 0 , W A C = 0 , W A D < 0

E A B = E A C < E A D , W A B > 0 , W A C = 0 , W A D < 0

E A B < E A C < E A D , W A B > 0 , W A C > W A D

E A B > E A C > E A D , W A B < W A C < W A D

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An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section $8.0 \times 1 0^{- 3} m^{2}$ . Initially the gas is at 300K and occupies a volume of $2.4 \times 1 0^{- 3} m^{3}$ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is $1.0 \times 1 0^{5} N / m^{2} .$ The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be :
(Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible)

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Important Questions on Thermodynamics

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

Which of the following statement is incorrect

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

A one mole of ideal gas goes through a process in which pressure

P

varies with volume

V

P = 3 - g {(\frac{V}{V_{0}})}^{2}

, where

V_{0}

is a constant. The maximum attainable temperature by the ideal gas during this process is (All quantities are in

SI

units and

R

is gas constant)

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

Consider the following thermodynamical variables
(i) Pressure
(ii) Internal Energy
(iii) Volume
(iv) Temperature

Out of these, the intensive variable(s) is (are)

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

In the case of black body for energy distribution, energy radiated by a blackbody which is given by, Planck's formula reduces to Rayleigh Jean's formula for

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

A balloon is filled at

27 ° C

and

1 atm

pressure by

500 m^{3}

He

. At

- 3 ° C

and

0.5 atm

pressure, the volume of

He

will be

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

The Clausius-Clayperon equation helps to calculate

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

Consider the given diagram. An ideal gas is contained in a chamber (left) of volume $V$ and is at an absolute temperature $T .$ It is allowed to rush freely into the right chamber of volume $V$ which is initially vacuum. The whole system is thermally isolated. What will be the final temperature, if the equilibrium has been attained?

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MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

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.

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

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

The pressure versus temperature graph of an ideal gas is shown in the figure below. If the density of gas at point $A$ is $ρ_{0}$ , then the density of the gas at point $B$ will be

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

A system goes from $A$ to $B$ via two processes $I$ and $II$ shown in the figure. If $Δ U_{1}$ and $Δ U_{2}$ are the changes in internal energies in the processes I and Il respectively

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HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

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

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure

1

). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (Figure

2

), the volume (in

m^{3}

) of the compartment A after the system attains equilibrium is

\frac{20}{x} m^{3}

. Write the value of

x

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

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

) ?

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

If system

A

is in thermal equilibrium with

B

and

B

is separately in thermal equilibrium with

C,

then

A

and

C

are in thermal equilibrium. From which thermodynamics law, does this follow?

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

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

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

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:

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

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>Thermal Equilibrium

Pressure versus temperature graph of an ideal gas at constant volume $V$ is shown by the straight-line $A$ . Now mass of the gas is doubled and the volume is halved then the corresponding pressure versus temperature graph will be shown by the line

Question Image

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

Three different processes that can occur in an ideal monoatomic gas are shown in the $P$ vs $V$ diagram. The paths are labelled as $A \to B, A \to C$ and $A \to D$ . The change in internal energies during these process are taken as $E_{A B}, E_{A C}$ and $E_{A D}$ and the work done as $W_{A B}, W_{A C}$ and $W_{A D}$ . The correct relation between these parameters are:

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermal Equilibrium

n

moles of an ideal gas undergoes a process

A \to B

as shown in the figure. The maximum temperature of the gas during the process will be:
Question Image

Important Questions on Thermodynamics

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