EASY

Earn 100

What is the internal energy for an isothermal process.

Important Questions on Thermodynamics

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

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>Thermodynamics>Thermodynamics State Variables and Equation of State

Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non- expansion work is zero)

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

The correct option for free expansion of an ideal gas under adiabatic condition is

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

A sample of an ideal gas undergoes an isothermal process as shown by the curve $A B$ in the $p V$ diagram. If $Δ Q, Δ U$ and $Δ W$ represent the amount of heat absorbed the change in internal energy and the work done respectively, then which of the following statement is correct?

Question Image

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

An engine operates by taking

n

moles of an ideal gas through the cycle

A B C D A

shown in figure. The thermal efficiency of the engine is:

(Take

C_{v} = 1.5 R

, where

R

is gas constant)

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

The figure shows the graph of $\frac{p V}{T}$ versus $p$ for $2 \times 10^{- 4} kg$ of hydrogen gas at two different temperatures, where $p, V$ and $T$ represents pressure, volume and temperature respectively.Then, the value of $\frac{p V}{T},$ where the curve meet on the vertical axis, is

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

Starting at temperature

300 K,

one mole of an ideal diatomic gas

(γ = 1.4)

is first compressed adiabatically from volume

V_{1}

V_{2} = \frac{V_{1}}{16} .

It is then allowed to expand isobarically to volume

2 V_{2}

. If all the processes are the quasi-static then the final temperature of the gas (in

K

) is (to the nearest integer) ___________.

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

For an ideal gas, the internal energy is given by

U = 5 p V / 2 + C,

where

C

is a constant. The equation of the adiabats in the

p V

-plane will be

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

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

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

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?

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

The Volume

(V)

of a monoatomic gas varies with its temperature

(T)

, as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state

A

to state

B

, is

EASY

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

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>Thermodynamics>Thermodynamics State Variables and Equation of State

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 is the correct combination?

HARD

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume

u = \frac{U}{V} \propto T^{4}

and pressure

p = \frac{1}{3} (\frac{U}{V})

. If the shell now undergoes an adiabatic expansion the relation between T and R is:

MEDIUM

Physics>Heat and Thermodynamics>Thermodynamics>Thermodynamics State Variables and Equation of State

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