22 g of carbon dioxide at `27^(@)C` is mixed in a closed container with 16 g of oxygen at `37^(@)C`. If both gases are considered as ideal gases, then the temperature of the mixture is

Options

A. `24.2 ^(@) C `
B. `28.5 ^(@) C`
C. `31.5 ^(@) C `
D. `33.5 ^(@) C`

Answer

C

Explanation

For carbon dioxide, number of moles
`(n _(1)) = (22)/(44) = (1)/(2)`
Molar specific heat of `CO _(2)` at constant volume `C _(V1) = (5 R)/(2)`
For oxygen, number of moles
`(n _(2)) = (16)/(32) = (1)/(2)`
Molar specific heat of `O _(2)` at constant volume ` C _(V 2)= ( 5 R)/(2)`
Let TK be the temperature of mixture.
Heat lost by`O _(2)` = Heat gained by `CO _(2)`
`n _(2) C_(V 2 ) Delta T _(2) = n _(1) C _(V 1) Delta T _(1)`
`( 1)/(2) (( 5)/(2) R) (310 - T) = (1)/(2)`
` xx (( 5 R)/(2)) ( T - 300)`
`2 T = 610`
` T = (610)/( 2) = 305 K = 32^(@) C`