Figure below shows two paths that may be taken by a gas to go from a state A to a state C. 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

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Solution

Q.
Figure below shows two paths that may be taken by a gas to go from a state A to a state C. 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 [2015]

1 460 J

2 300 J

3 380 J

4 500 J

Ans.
(1)

As initial and final points for two paths are same so

$Δ U_{A B C} = Δ U_{A C}$

AB is isochoric process.

$Δ W_{A B} = 0$

$∆ Q_{A B} = Δ U_{A B} = 400$ $J$

BC is isobaric process.

$Δ Q_{B C} = Δ U_{B C} + Δ W_{B C}$

$100 = Δ U_{B C} + 6 \times 10^{4} (4 \times 10^{- 3} - 2 \times 10^{- 3})$

$100 = Δ U_{B C} + 12 \times 10$

$Δ U_{B C} = 100 - 120 = - 20$ $J$

As, $Δ U_{A B C} = Δ U_{A C}, Δ U_{A B} + Δ U_{B C} = Δ Q_{A C} - Δ W_{A C}$

$400 - 20 = Δ Q_{A C} - (2 \times 10^{4} \times 2 \times 10^{- 3} + \frac{1}{2} \times 2 \times 10^{- 3} \times 4 \times 10^{4})$

$Δ Q_{A C} = 460$ $J$

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