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

Question

An ideal gas is taken from state 1 to state 2 through optional path A, B, C and D as shown in the P V diagram. Let Q, W and U represent the heat supplied, work done and change in internal energy of the gas respectively. Then, (A) QA-QD=WA-WD (B) QB-WB > QC-WC (C) WA < WB < WC < WD (D) QA < QB < QC < QD

Tardigrade Admin · Accepted Answer

Work done by gas in all four process is positive and in order

W_{A} > W_{B} > W_{C} > W_{D}

\Rightarrow

(c) is false
The change in initial energy

U

is same for all process.

∴ Q_{A} = U + W_{A}

...(1)

Q_{B} = U + W_{B}

...(2)

Q_{C} = U + W_{C}

...(3)

Q_{D} = U + W_{D}

...(4)
Hence

Q_{A} > Q_{B} > Q_{C} > Q_{D}

\Rightarrow

(d) is false
from equations (1) and (4)

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

\Rightarrow

(a) is true
from equations (2) and (3)

Q_{B} - Q_{C} = W_{B} - W_{C}

\Rightarrow

(b) is false.

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

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

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

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

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

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

QA​−QD​=WA​−WD​

QB​−WB​>QC​−WC​

WA​<WB​<WC​<WD​

QA​<QB​<QC​<QD​

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

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

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

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

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