Question 570: Thermodynamics & KTG

Question

Starting at temperature 300 K, one mole of an
ideal diatomic gas ($$\gamma $$ = 1.4) is first compressed
adiabatically from volume V
1
to V
2
= $${{{V_1}} \over {16}}$$. It is
then allowed to expand isobarically to volume
2V
2
. If all the processes are the quasi-static then
the final temperature of the gas (in
o
K) is (to
the nearest integer) _____.

Accepted Answer

T
1
V
1
$$\gamma $$Ã¢ÂÂ1
= T
2
V
2
$$\gamma $$Ã¢ÂÂ1
$$300 	imes {V^{{7 \over 5} - 1}} = {T_2}{\left( {{V \over {16}}} ight)^{{7 \over 5} - 1}}$$
$$ \Rightarrow $$ T
2
= 300 ÃÂ (16)
0.4
Isobaric process
V = $${{nRT} \over P}$$
V
2
= kT
2
... (1)
2V
2
= KT
f
... (2)
T
f
= 2T
2
= 300 ÃÂ 2 ÃÂ (16)
0.4
= 1818 K

Thermodynamics & KTG

Integer / Numeric Answer Type