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

Explain why (a) Two bodies at different temperatures T 1 and T 2 if brought in thermal contact do not necessarily settle to the mean temperature ( T 1 + T 2 )/2.

Till equilibrium is achieved, heat flows from the body at the higher temperature to the body at the lower temperature when two bodies at different temperatures T l and T 2 are brought in thermal contact, i.e., the temperatures of both the bodies become the same. The equilibrium temperature is the same as the mean temperature ( T 1 + T 2 ) 2 only when the thermal capacities of both bodies are equal.

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Important Questions on Heat and Thermodynamics

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

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

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EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

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

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

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

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:

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HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

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)

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

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>Heat and Thermodynamics>Zeroth Law of Thermodynamics

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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MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

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:
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MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

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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EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

Diagram shows a horizontal cylindrical container of length $30 cm$ , which is partitioned by a tight-fitting separator. The separator is diathermic but conducts heat very slowly. Initially the separator is in the state shown in the diagram. The temperature of left part of cylinder is $100 K$ and that on right part is $400 K$ . Initially the separator is in equilibrium. As heat is conducted from right to left part, separator displaces to the right. Find the displacement of separator(in $cm$ ) after a long time when gases on the two parts of cylinder are in thermal equilibrium.

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EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

There are four objects A, B, C and D. It is observed that A and B are in thermal equilibrium and C and D are also in thermal equilibrium. However, A and C are not in thermal equilibrium. We can conclude that

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

An ideal gas can be expanded from an initial state to a certain volume through two different processes

(i) P V^{2} =

constant and

(ii) P = K V^{2}

where

K

is a positive constant. Then

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

Explain why

(a) Two bodies at different temperatures T₁ and T₂ if brought in thermal contact do
not necessarily settle to the mean temperature (T₁ + T₂ )/2.

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

In the arrangement shown in figure. Gas is thermally insulated. An ideal gas is filled in the cylinder having pressure $P_{0}$ (> atmospheric pressure $Pa$ ). Spring of force constant $k$ is initially unstretched. Piston of mass $m$ and area $S$ is frictionless. In equilibrium piston rises up a distance $x_{0}$ , then
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MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

The thermo emf E (in volts) of a certain thermocouple is found to vary with Q (in C) according to equation

(E = 20 Q - \frac{Q^{2}}{20},) where Q

is temperature of the hot function, the cold function being kept at

0^{o} C

. Then, the neutral temperature of the thermocouple is

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

One mole of an ideal gas at pressure

P_{0}

and temperature

T_{0}

is expanded isothermally to twice its volume and then compressed at constant pressure to

(\frac{V_{0}}{2})

and the gas is brought back to original state by a process in which

P \propto V

(pressure is directly proportional to volume). The correct temperature of the process is

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Zeroth Law of Thermodynamics

Two rigid boxes containing different ideal gases are placed on table. Box A contains one mole of nitrogen at temperature

T_{0}

, while box B contains 1 mole of helium at temperature

\frac{7}{3} T_{0} .

The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes) then the final temperature of gases,