Question 1: Thermodynamics & KTG

Question

An ideal gas is expanding such that PT$^2$ = constant. The coefficient of volume expansion of the gas is

Accepted Answer

Given, PT$^2$ = constant ..... (i)
For an ideal gas,
$\frac{\mathrm{PV}}{\mathrm{T}}$ = constant ...... (ii)
From above two equation, after eliminating P.
$\frac{\mathrm{V}}{\mathrm{T^3}}$ = Constant
$\Rightarrow$ V = KT$^3$, where $k$ = constant.
$\frac{d\mathrm{V}}{\mathrm{V}}=3\frac{d\mathrm{T}}{\mathrm{T}}$
$ \Rightarrow dV = \left( {{3 \over T}} \right)VdT$ ..... (iii)
Change in volume due to thermal expansion is given by $dV=Vydt$ ..... (iv)
Where, $y$ = coefficient of volume expansion
From equation (iii) and (iv), we have,
$VydT = \left( {{3 \over T}} \right)VdT$
$ \Rightarrow y = {3 \over T}$

Answer

$\frac{1}{\mathrm{T}}$

Answer

$\frac{2}{\mathrm{T}}$

Answer

$\frac{3}{\mathrm{T}}$

Answer

$\frac{4}{\mathrm{T}}$

Thermodynamics & KTG

An ideal gas is expanding such that PT^2 = constant. The coefficient of volume expansion of the gas is

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