An ideal gas is expanding such that P T= constant. The coefficient of volume expansion of the gas is

Question

An ideal gas is expanding such that P T= constant. The coefficient of volume expansion of the gas is (A) (1/T) (B) (2/T) (C) (3/T) (D) (4/T)

Tardigrade Admin · Accepted Answer

P T= Constant or (T2/V)= Constant [P V=n R T] ⇒ T2=K V ldots (i) Differentiating w.r.t. T, we get (2 T/V)-(K/V) (d V/d T) ⇒ (2 T/V K)=(d V/V d T) ∴ (d V/V d T)=(2 T V/V T2)=(2/T)

Q. An ideal gas is expanding such that $PT =$ constant. The coefficient of volume expansion of the gas is

$\frac{1}{T}$

$\frac{2}{T}$

$\frac{3}{T}$

$\frac{4}{T}$

$PT =$ Constant
or $\frac{T ^{2}}{V} =$ Constant
$[P V = n RT]$
$\Rightarrow T_{2} = K V \dots$ (i)
Differentiating w.r.t. $T$ , we get
$\frac{2 T}{V} - \frac{K}{V} \frac{d V}{d T}$
$\Rightarrow \frac{2 T}{V K} = \frac{d V}{V d T}$
$∴ \frac{d V}{V d T} = \frac{2 T V}{V T ^{2}} = \frac{2}{T}$

Q. An ideal gas is expanding such that PT= constant. The coefficient of volume expansion of the gas is

T1​

T2​

T3​

T4​