CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

1st Law of Thermodynamics

Four identica...

Question

Four identical samples of an ideal gas are taken along the paths $A, B, C$ and $D$ from state $1$ to state $2$ as shown in the $P V$ indicator diagram. Let $Q, W$ and $Δ U$ represent the heat supplied, work done and change in internal energy of the gas respectively. Choose the correct option among the following :

A

Q_{A} - Q_{D} = W_{A} - W_{D}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

Q_{B} - W_{B} > Q_{C} - W_{C}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

W_{A} < W_{B} < W_{C} < W_{D}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

Q_{A} < Q_{B} < Q_{C} < Q_{D}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $Q_{A} - Q_{D} = W_{A} - W_{D}$
We know that area under $P - V$ curve gives the work done during the process.
Work done by the gas in all four processes is positive and is in the order
$W_{A} > W_{B} > W_{C} > W_{D} . . . . . (1)$
Hence, option (c) is wrong.
The change in internal energy $Δ U$ is the same for all processes as initial and final states for all processes are the same.
Using first law of thermodynamics for each process $A, B, C$ and $D$ , we get
$Q_{A} = Δ U + W_{A} . . . . . . (2)$
$Q_{B} = Δ U + W_{B} . . . . . . (3)$
$Q_{C} = Δ U + W_{C} . . . . . . (4)$
$Q_{D} = Δ U + W_{D} . . . . . . (5)$
Hence, from $(1)$ we can say that, $Q_{A} > Q_{B} > Q_{C} > Q_{D}$
So, option (d) is also wrong.

From equation $(3)$ and $(4)$ ,
$Q_{B} - Q_{C} = W_{B} - W_{C}$
$\Rightarrow Q_{B} - W_{B} = Q_{C} - W_{C}$
i.e option (b) is wrong.

From equation $(2)$ and $(5)$ ,
$Q_{A} - Q_{D} = W_{A} - W_{D}$
Thus, option (a) is the correct answer.

Suggest Corrections

thumbs-up

1

Similar questions

Q. Four identical samples of an ideal gas are taken along the paths

A, B, C

D

1

2

as shown in the

P V

indicator diagram. Let

Q, W

Δ U

represent the heat supplied, work done and change in internal energy of the gas respectively. Choose the correct option among the following :

Q. An ideal gas is taken from state 1 to state 2 through optional path A, B , C & D as shown in P-V diagram. Let Q, W and U represent the heat supplied, work done & internal energy of the gas respectively. Then

Q. A sample of ideal gas goes from state

A

B

for as shown in the graph. Let

W

be the work done by gas and

Δ U

be the change in internal energy along the path

AB

. Identify the correct statement.

Q. In the following diagram the work done in moving a point charge from point P to point A, P to B and P to C is respectively

W_{A}

W_{B}

W_{C}

Q. Refer to the Carnot cycle of an ideal gas shown in the figure Let

W_{a \to b}, W_{b \to c}, W_{c \to d}

W_{d \to a}

represent the work done by the system during the processes

a \to b, b \to c, c \to d

d \to a

respectively. Consider the following relations
(1)

W_{a \to b} + W_{b \to c} + W_{c \to d} + W_{d \to a} > 0

W_{a \to b} + W_{b \to c} + W_{c \to d} + W_{d \to a} < 0

W_{a \to b} + W_{c \to d} > 0

W_{b \to c} + W_{d \to a} = 0

Which of the above relation is/are true

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

1st Law of Thermodynamics

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon