JAMB - Physics (1983 - No. 12)
If the pressure on 100cm3 of an ideal gas is doubled while its kelvin temperature is halved, then the new volume of the gas will become
25cm3
50cm3
100cm3
200cm3
400cm3
Explanation
\(\frac{P_1V_1}{T_1}\) = \(\frac{P_2V_2}{T_2}\)
P\(_2\) = 2P\(_1\) ; T\(_1\) = 2T\(_2\)
V\(_2\) = \(\frac{P_1 \times V_1 \times T_2}{T_1 \times P_2}\) = \(\frac{P_1 \times 100 \times T_2}{2T_2 \times 2P_1}\) = \(\frac{100}{4}\)
= 25cm\(^3\)
P\(_2\) = 2P\(_1\) ; T\(_1\) = 2T\(_2\)
V\(_2\) = \(\frac{P_1 \times V_1 \times T_2}{T_1 \times P_2}\) = \(\frac{P_1 \times 100 \times T_2}{2T_2 \times 2P_1}\) = \(\frac{100}{4}\)
= 25cm\(^3\)
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