First slide

Different type of processes

Question

Argon gas is adiabatically compressed to half its volume. If P, V and T represent the pressure, volume and temperature of the gaseous system, respectively, at any stage, then the correct equation representing the process is

Moderate

A

${TV}^{2 / 5} - constant$
B

${VP}^{5 / 3} = constant$
C

${TP}^{- 2 / 5} = constant$
D

${PT}^{2 / 5} = constant$

Solution

For an adiabatic process,
${PV}^{Y}$ = constant
${TV}^{γ - 1}$ = constant
and $T^{γ} P^{1 - γ}$ = constant
Putting, γ = 5/3 (argon being a monatomic gas), the equation becomes:
${PV}^{5 / 3} =$ constant
${TV}^{- 2 / 3} =$ constant
$T^{5 / 3} P^{- 2 / 3} =$ constant ⇒ ${TP}^{- 2 / 5} =$ constant

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