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Question

Figure below shows two paths that may be taken by a gas to go from a state A to a state C.
In process A B, 400 J of heat is added to the system and process B C, 100 J of heat is added to the system. The heat absorbed by the system in the process A C will be

Difficult

A

460 J
B

300 J
C

380 J
D

500 J

Solution

As initial and final points are same so
${ΔU}_{ABC} = {ΔU}_{AC} AB is isochoric process. \begin{array}{l} {ΔW}_{AB} = 0 \\ {ΔQ}_{AB} = {ΔU}_{AB} = 400 J \end{array} BC is isobaric process. \begin{array}{l} {ΔQ}_{BC} = {ΔU}_{BC} + {ΔW}_{BC} \\ 100 = {ΔU}_{BC} + 6 \times 10^{4} (4 \times 10^{- 3} - 2 \times 10^{- 3}) \\ 100 = {ΔU}_{BC} + 12 \times 10 \\ {ΔU}_{BC} = 100 - 120 = - 20 J \\ As, {ΔU}_{ABC} = {ΔU}_{AC} \end{array} {ΔU}_{AB} + {ΔU}_{BC} = {ΔQ}_{AC} - {ΔW}_{AC}$
$\begin{array}{r} 400 - 20 = {ΔQ}_{AC} - (2 \times 10^{4} \times 2 \times 10^{- 3} + \\ \frac{1}{2} \times 2 \times 10^{- 3} \times 4 \times 10^{4}) \\ 380 = {ΔQ}_{AC} - (40 + 40), {ΔQ}_{AC} = 380 + 80 = 460 J \end{array}$

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