An ideal gas is initially at temperature and volume . Its volume is increased by due to an increase in temperature , pressure remaining constant. The quantity varies with temperature as [2000]

Question

An ideal gas is initially at temperature $T$ and volume $V$ . Its volume is increased by $Δ V$ due to an increase in temperature $Δ T$ , pressure remaining constant. The quantity $δ = \frac{Δ V}{V Δ T}$ varies with temperature as [2000]

Smart Achievers · Accepted Answer

(3)

For a given mass of gas at constant pressure,

$\frac{V}{T} = Constant$ $δ = \frac{Δ V}{V Δ T}$ $\frac{V + Δ V}{T + Δ T} = \frac{V}{T}$

or $V T + V Δ T = V T + T Δ V$ or $V Δ T = T Δ V$

or $\frac{1}{T} = \frac{Δ V}{V Δ T}$ or $\frac{1}{T} = δ$ or $δ T = 1$

The equation represents a rectangular hyperbola of the form $x y = c^{2}$ depicted by graph (3).

Solution

Q.
An ideal gas is initially at temperature $T$ and volume $V$ . Its volume is increased by $Δ V$ due to an increase in temperature $Δ T$ , pressure remaining constant. The quantity $δ = \frac{Δ V}{V Δ T}$ varies with temperature as [2000]

1

2

3

4

Want Us to Email you About Special Offers & Updates?

Solution

Q. An ideal gas is initially at temperature T and volume V. Its volume is increased by ΔV due to an increase in temperature ΔT, pressure remaining constant. The quantity δ=ΔVVΔT varies with temperature as [2000]

1

2

3

4

Ans. (3) For a given mass of gas at constant pressure, VT=Constant ∴ V+ΔVT+ΔT=VT or VT+VΔT=VT+TΔV or VΔT=TΔV or 1T=ΔVVΔT or 1T=δ or δT=1 The equation represents a rectangular hyperbola of the form xy=c2 depicted by graph (3).

Want Us to Email you About Special Offers & Updates?

Q.
An ideal gas is initially at temperature $T$ and volume $V$ . Its volume is increased by $Δ V$ due to an increase in temperature $Δ T$ , pressure remaining constant. The quantity $δ = \frac{Δ V}{V Δ T}$ varies with temperature as [2000]