Question

In an adiabatic process if pressure P and density
d of a monatomic gas are related as P is
proportional to d^x, then x is equal to
1.2/7
2.3/5
3.5/2
4.5/3 answer is 5 by 3​

Answer 1

Answer:we only need to compare the given equation with the adiabatic equation.

Explanation:

Answer 2

answer : option (4) 5/3

explanation : in adiabatic process, ∆Q = 0

and relation between pressure and volume is given as, $PV^{\gamma}=K$, where $\gamma$ is atomicity of given ideal gas.

here it is given that, P ∝ d^x .......(1)

but we know, density , d = mass/volume

mass remains same. so, d ∝ 1/V

or, d^x ∝ 1/V^x .......(2)

from equations (1) and (2),

P ∝ 1/V^x ⇒PV^x ∝ 1 means, PV^x = constant.

on comparing with $PV^{\gamma}=K$

we x = $\gamma$

now for monoatomic gas, $\gamma$ = 5/3

so, x = $\gamma$ = 5/3

hence, option (4) is correct choice.