An ideal gas at pressure P and temperature T is expanding such that . The coefficient of volume expansion of the gas is

Question

An ideal gas at pressure P and temperature T is expanding such that $P T^{3} = constant$ . The coefficient of volume expansion of the gas is ______. [2026]

Smart Achievers · Accepted Answer

(3)

$P T^{3} = k (constant)$

$(\frac{n R T}{V}) T^{3} = k \Rightarrow V = (\frac{n R}{k}) T^{4}$

$Volume expansion coefficient, γ = \frac{1}{V} (\frac{d V}{d T})$

$γ = \frac{k}{n R T^{4}} \cdot (\frac{n R}{k}) \cdot 4 T^{3} = \frac{4}{T}$

Solution

Q.
An ideal gas at pressure P and temperature T is expanding such that $P T^{3} = constant$ . The coefficient of volume expansion of the gas is ______. [2026]

1 $\frac{2}{T}$

2 $\frac{1}{T}$

3 $\frac{4}{T}$

4 $\frac{3}{T}$

Ans.
(3)

$P T^{3} = k (constant)$

$(\frac{n R T}{V}) T^{3} = k \Rightarrow V = (\frac{n R}{k}) T^{4}$

$Volume expansion coefficient, γ = \frac{1}{V} (\frac{d V}{d T})$

$γ = \frac{k}{n R T^{4}} \cdot (\frac{n R}{k}) \cdot 4 T^{3} = \frac{4}{T}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. An ideal gas at pressure P and temperature T is expanding such that PT3=constant. The coefficient of volume expansion of the gas is ______. [2026]

1 2T

2 1T

3 4T

4 3T

Ans. (3) PT3=k (constant) (nRTV)T3=k⇒V=(nRk)T4 Volume expansion coefficient, γ=1V(dVdT) γ=knRT4·(nRk)·4T3=4T