A gas mixture contains 1.00 mol He and 2.00 mol O2 (treat O2 as a rigid diatomic ideal gas with vibrations frozen; R = 8.314 J mol^-1K^-1). Which statements are correct?

The total C_V of the mixture is about 54.0 J K^-1.

The gamma of the mixture equals 1.40.

Heating the mixture by 10.0 K at constant pressure needs about 540 J.

On reversible adiabatic compression to half the volume from 300 K, the final temperature is about 413 K.

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3td031

A gas mixture contains $1.00 mol$ He and $2.00 mol$ $O X_{2}$ (treat $O X_{2}$ as a rigid diatomic ideal gas with vibrations frozen; $R = 8.314 J mo l^{- 1} K^{- 1}$ ). Which statements are correct?

AThe total $C_{V}$ of the mixture is about $54.0 J K^{- 1}$ .
BThe $γ$ of the mixture equals $1.40$ .
CHeating the mixture by $10.0 K$ at constant pressure needs about $540 J$ .
DOn reversible adiabatic compression to half the volume from $300 K$ , the final temperature is about $413 K$ .

C_{V} = 1 (\frac{3}{2} R) + 2 (\frac{5}{2} R) = 6.5 R = 54.04 J K^{- 1}

(A true).

C_{P} = C_{V} + 3 R = 8.5 R

, so

γ = 8.5/6.5 = 1.462

, not

1.40

(B false). Constant-pressure heat for

10 K

8.5 R (10) = 790 J

;

540 J

is the constant-volume value (C false).

T_{2} = 300 \times 2^{γ - 1} = 413.1 K

(D true).