Question

Two moles of an ideal diatomic gas occupies a volume V at 27° C. The gas expands adiabatically to a volume 2V. Calculate the final temperature of the gas is nearly ____________.

Options

• 89 K

• 195 K

• 228 K

• 395 K

Answer 1

Two moles of an ideal diatomic gas occupies a volume V at 27° C. The gas expands adiabatically to a volume 2V. Calculate the final temperature of the gas is nearly 228 K.

Explanation:

Given: T₁ = 27° C = 273 + 27 = 300 K,

`"V"_2/"V"_1 = 2`

For adiabatic process,

`"TV"^(gamma - 1) = "constant"`

`therefore "T"_1  "V"_1^(gamma - 1) = "T"_2  "V"_2^(gamma - 1)`

`gamma = 7/5` for diatomic gas.

`therefore "T"_2/"T"_1 = ("V"_1/"V"_2)^(gamma-1)`

`= (1/2)^(7/5-1) = (1/2)^(2/5) = (1/4)^(1/5) approx  0.76`

`therefore "T"_2 = "T"_1 xx 0.76`

`therefore "T"_2 = 300 xx 0.76 approx 228 "K"`