Question 618: Thermodynamics & KTG

Question

Initially a gas of diatomic molecules is contained in a cylinder of volume V1
 at a pressure P1
 and
temperature 250 K. Assuming that 25% of the molecules get dissociated causing a change in
number of moles. The pressure of the resulting gas at temperature 2000 K, when contained in a
volume 2V1
 is given by P2
. The ratio $${{{P_2}} \over {{P_1}}}$$
 is ________.

Accepted Answer

We know, PV = nRT
$$ 	herefore $$ P
1
V
1
= nR (250)
and P
2
(2V
1
) = $${{5n} \over 4}R 	imes \left( {2000} ight)$$
By Dividing
$${{{P_1}} \over {2{P_2}}}$$ = $${{4 	imes 250} \over {5 	imes 2000}}$$
$$ \Rightarrow $$ $${{{P_1}} \over {{P_2}}} = {1 \over 5}$$
$$ \Rightarrow $$ $${{{P_2}} \over {{P_1}}} = 5$$

Thermodynamics & KTG

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