Question

16. If a gas is taken from A to C through B then heat
absorbed by the gas is 8 J. Heat absorbed by the
gas in taking it from A to C directly is
P (kPa)
200
(1) 8 J
(3) 11 J
400 V (cc)
29 J
(4) 12 J​

Answer 1

$Q_{AC}=9\ J$ is the work done in taking the gas directly from A to C.

Explanation:

Given:

• Pressure at point A,  $P_A=10000\ Pa$

• Pressure at point B,  $P_B=10000\ Pa$

• Pressure at point C,  $P_C=20000\ Pa$

• Volume at point A,  $V_A=2\times 10^{-4}\ m^3$

• Volume at point B,  $V_B=4\times 10^{-4}\ m^3$

• Volume at point C,  $V_C=4\times 10^{-4}\ m^3$

• Heat absorbed by the system, $Q_{ABC}=8\ J$

Now work done from A to C via B:

$W_{ABC}=10000\times (4\times 10^{-4}-2\times 10^{-4})$

$W_{ABC}=2\ J$

Using first law of thermodynamics:

$Q_{ABC}=W_{ABC}+\Delta U$

$8=2+\Delta U$

$\Delta U=6\ J$

Now the work done via A to C directly:

$W_{AC}=\frac{1}{2} (10000+20000)\times 2\times 10^{-4}$

$W_{AC}=3\ J$

Now apply the first law of thermodynamics:

$Q_{AC}=W_{AC}+\Delta U$

$Q_{AC}=3+6=9\ J$

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TOPIC: Thermodynamics first law

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