A fixed amount of a gas undergoes a thermodynamic process as show… - Vidyadip

MCQ

A fixed amount of a gas undergoes a thermodynamic process as shown such that heat interaction along path $B \to C \to A$ is equal to the work done by the gas along path $A \to B \to C$. Then process $A \to B$ is :-

A
can only be isothermal
✓
can only be adiabatic
C
can be isothermal or adiabatic
D
none of the above

✓

Answer

Correct option: B.

can only be adiabatic

b
As process is cyclic $\Rightarrow \Delta \mathrm{U}_{\mathrm{ABCA}}=0$

$\Rightarrow \mathrm{Q}_{\mathrm{ABCA}}=\mathrm{W}_{\mathrm{ABCA}}$

$\Rightarrow \mathrm{Q}_{\mathrm{A} \rightarrow \mathrm{B}}+\mathrm{Q}_{\mathrm{B} \rightarrow \mathrm{C}}+\mathrm{Q}_{\mathrm{C} \rightarrow \mathrm{A}}$

$=\mathrm{W}_{\mathrm{A} \rightarrow \mathrm{B}}+\mathrm{W}_{\mathrm{B} \rightarrow \mathrm{C}}+\mathrm{W}_{\mathrm{C} \rightarrow \mathrm{A}}$ $.(1)$

Given $Q_{B \rightarrow C}+Q_{C \rightarrow A}=W_{A \rightarrow B}+W_{B \rightarrow C}$ $(2)$

Subtracting $( 2)$ from $( 1)$

$\mathrm{Q}_{\mathrm{A} \rightarrow \mathrm{B}}=\mathrm{W}_{\mathrm{C} \rightarrow \mathrm{A}}=0$

(as process $\mathrm{C} \rightarrow \mathrm{A}$ is isochoric)

process $A \rightarrow B$ is adiabatic.

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