JEE MAIN - Physics (2020 - 6th September Morning Slot - No. 21)
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 ________.
Answer
5
Explanation
We know, PV = nRT
$$ \therefore $$ P1V1 = nR (250)
and P2(2V1) = $${{5n} \over 4}R \times \left( {2000} \right)$$
By Dividing
$${{{P_1}} \over {2{P_2}}}$$ = $${{4 \times 250} \over {5 \times 2000}}$$
$$ \Rightarrow $$ $${{{P_1}} \over {{P_2}}} = {1 \over 5}$$
$$ \Rightarrow $$ $${{{P_2}} \over {{P_1}}} = 5$$
$$ \therefore $$ P1V1 = nR (250)
and P2(2V1) = $${{5n} \over 4}R \times \left( {2000} \right)$$
By Dividing
$${{{P_1}} \over {2{P_2}}}$$ = $${{4 \times 250} \over {5 \times 2000}}$$
$$ \Rightarrow $$ $${{{P_1}} \over {{P_2}}} = {1 \over 5}$$
$$ \Rightarrow $$ $${{{P_2}} \over {{P_1}}} = 5$$
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