Starting at temperature 300K, one mole of an ideal diatomic gas (γ...

Starting at temperature

300K,

one mole of an ideal diatomic gas

\left(\gamma = 1.4\right)

is first compressed adiabatically from volume

{V}_{1} to {V}_{2} = \dfrac{{V}_{1}}{16} .

It is then allowed to expand isobarically to volume

2{V}_{2}

. If all the processes are the quasi-static then the final temperature of the gas (in

{}^{o}K

) is (to the nearest integer) ___________. Starting at temperature 300K, one mole of an ideal diatomic gas (γ = 1.4) is first compressed adiabatically from volume

Correct answer

Step-by-step solution

P{V}^{y} = constant

T{V}^{- 1} = constant

300{\left({V}_{1}\right)}^{1.4 - 1} = {T}_{B}{\left(\dfrac{{V}_{1}}{16}\right)}^{2 / 5}

{T}_{B} = 300 \times {2}^{8 / 5}

Now for BC process

\dfrac{{V}_{B}}{{T}_{B}} = \dfrac{{V}_{c}}{{T}_{c}}

{T}_{c} = \dfrac{{V}_{c}{T}_{B}}{{v}_{B}} = 2 \times 300 \times {2}^{8 / 5}

{T}_{c} = 1818.859

{T}_{c} = 1819K

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