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Relation between P, V, T, Gamma in Adiabatic Proceses

Temperature o...

Question

Temperature of a monoatomic gas is increased from $T_{0}$ to $2 T_{0}$ in three different processes : isochoric, isobaric and adiabatic. Heat given to the gas in these processes are $Q_{1}, Q_{2}$ and $Q_{3}$ respectively. Then choose the correct option.

A

Q_{1} > Q_{3}

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B

Q_{2} > Q_{1}

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C

Q_{2} > Q_{3}

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D

Q_{3} = 0

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Solution

The correct options are
A $Q_{1} > Q_{3}$
B $Q_{2} > Q_{1}$
C $Q_{2} > Q_{3}$
D $Q_{3} = 0$
First law of thermodynamics gives us the relation:
$q = Δ U + w$
For all three cases $Δ U$ is the same (only a function of temperature).
For isochoric w = 0;
For adiabatic w $= Δ U$
For isobaric w = positive.
Work done is maximum in isobaric.
i.e.
$Q_{2} > Q_{1} > Q_{3}$
and $Q_{3} = 0$
Hence all four options are correct.

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