Question 45: Thermodynamics & KTG

Question

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

Accepted Answer

LetÃ¢ÂÂs find how V varies with T along the path PTÃÂ² = constant, then compute
the volumeÃ¢ÂÂexpansion coefficient
ÃÂ² = (1/V)(dV/dT).
From
$$P\,T^2=k\quad\Longrightarrow\quad P=\frac{k}{T^2}\,. $$
For one mole of an ideal gas,
$$P\,V=R\,T\quad\Longrightarrow\quad V=\frac{R\,T}{P}   =\frac{R\,T}{\,k/T^2\,}=\frac{R}{k}\,T^3\,. $$
Differentiate:
$$\frac{dV}{dT}=\frac{R}{k}\,3\,T^2\,. $$
Hence
$$\beta=\frac1V\frac{dV}{dT}  =\frac{1}{(R/k)\,T^3}\cdot\frac{3R}{k}\,T^2 =\frac{3}{T}\,. $$
Answer: 3/T  (Option D).

Answer

$\frac{2}{T}$

Answer

$3 T$

Answer

$\frac{T}{3}$

Answer

$\frac{3}{T}$

Thermodynamics & KTG

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

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