In the given graph, an ideal gas can change its state from A to C by two paths ABC or AC. Taking, the internal energy of gas at ‘A’ is 10 J, mark the CORRECT option(s)

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The amount of heat supplied in path AC is 200 J, then the internal energy of gas at ‘C’ is 75 J.

If the internal energy of gas at state B is 20 J. Then the amount of heat supplied to the gas to go from A to B may be 5 Joule.

The amount of heat supplied in path AC is 200 J, then the internal energy of gas at ‘C’ is 150 J.

If the internal energy of gas at state B is 20 J. Then the amount of heat supplied to the gas to go from A to B must be 10 Joule.

answer is A, D.

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Detailed Solution

In path $A \to C$
$W = 4 \times 10 + \frac{1}{2} \times 10 \times 4 = 40 + 20 = 60 J$
$Q = Δ U + W$
$200 = U_{C} - U_{A} + 60$
$U_{C} = 140 + U_{A} = 140 + 10 = 150 J$
In path $A \to B$
$Q_{A B} = U_{B} - U_{A} = U_{B} (1 - \frac{U_{A}}{U_{B}}) = U_{B} (1 - \frac{T_{A}}{T_{B}}) = 20 (1 - \frac{1}{2}) = 10 Joule$