Question

An ideal diatomic gas is taken through an adiabatic process in which density increases to 32 times. If the pressure increases to ‘n’ times. Find n.

Answer 1

An ideal diatomic gas is taken through an adiabatic process in which density increases to 32 times.

To find : if the pressure increases to n times find the value of n.

solution : for adiabatic process,

$PV^{\gamma}=constant$

let m is mass and ρ is density of gas.

so, V = m/ρ

then $P\left(\frac{m}{\rho}\right)^{\gamma}=constant$

⇒P ∝ ρ^γ

i.e., $\frac{P_1}{P_2}=\left(\frac{\rho_1}{\rho_2}\right)^{\gamma}$

for diatomic gas, γ = 7/5

P₂ = nP₁

ρ₂ = 32ρ₁

so, 1/n = (1/32)^(7/5) = (1/2)^7

⇒n = 2^7 = 128

Therefore the value of n is 128.i.e., option (4)