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During adiabatic expansion of 10 moles of a gas, the internal energy decreases by 50 J. Work done during the process is

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Important Questions on Thermodynamics

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

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

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

For the given cyclic process $C A B$ as shown for a gas, the work done is:

Question Image

MEDIUM

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

In a thermodynamic system,

Q

represents the energy transferred to or from a system by heat and

W

represents the energy transferred to or from a system by work

(I)

Q > 0

and

W = 0

(II)

Q < 0

and

W = 0

(III)

W > 0

and

Q = 0

(IV)

W < 0

and

Q = 0

Which of the above will lead to an increase in the internal energy of the system?

EASY

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

When a system is taken from state $i$ to state $f$ along the path $i a f$ , it is found that $Q = 50 cal$ and $W = 20 cal$ . Along the path $i b f$ , $Q' = 36 cal$ . $W$ along the path $i b f$ is,

Question Image

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?

EASY

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

Which of the following does not follow first law of thermodynamics?

(w =

work

; q =

heat

; ΔU =

change in internal energy

)

EASY

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

Five moles of an ideal monoatomic gas with an initial temperature of

150 ° C

expand and in the process absorb

1500 J

of heat and does

2500 J

of work. The final temperature of the gas in

° C

is (ideal gas constant,

R = 8.314 J K^{- 1} {mol}^{- 1}

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)?

EASY

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

Work done on (or) by a thermodynamic system is zero in which of the following processes?

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 diatomic gas undergoes a transition from $A$ to $B$ along a path $A B$ as shown in figure. The change in internal energy of the gas during the transition is

Question Image

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

The $P - V$ diagram shown below indicates two paths along which a sample of gas can be taken from state $A$ to state $B$ . The energy equal to $5 P V$ in the form of heat is required to be transferred if the Path- $1$ is chosen. How much energy in the form of heat should be transferred if Path- $2$ is chosen?

Question Image

MEDIUM

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

The internal energy of the air, in a room of volume

V

, at temperature

T

and with outside pressure

P

increasing linearly with time, varies as

HARD

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

Certain quantity of heat is supplied to a monatomic ideal gas which expands at constant pressure. The percentage of heat that is used to do work by the gas 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

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:

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:

During adiabatic expansion of 10 moles of a gas, the internal energy decreases by 50 J. Work done during the process is

Important Questions on Thermodynamics

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