Question

In an adiabatic change,the pressure p and temperature T of a diatomic gas are related by the relation P proportional to Tć where c is equal to
1) 5/3 2)2/5 3)3/5 4) 7/2

Answer 1

Relation change the pressure pressure and temperatures

Answer 2

Answer:

The value of constant is $\dfrac{5}{3}$

1. is correct option.

Explanation:

We know that,

For adiabatic change is

$PV^{\gamma}=constant$

Using equation of ideal gas

$PV= RT$

$V=\dfrac{RT}{P}$

Put the value of V in equation (I)

$P(\dfrac{RT}{P})^{\gamma}=constant$

$P^{1-\gamma}T^{\gamma}=constant$

Now, $P\propto T^{\dfrac{-\gamma}{1-\gamma}}$

The value of constant is

$constant = \dfrac{\gamma}{\gamma-1}$

The value of gamma for diatomic gas is

$\gamma=\dfrac{5}{2}$

$constant =\dfrac{\dfrac{5}{2}}{\dfrac{5}{2}-1}$

$constant = \dfrac{5}{3}$

Hence, The value of constant is $\dfrac{5}{3}$.