By what amount must the temperature of 200cm\(^3\) of Nitrogen at 27°C be increased to double the pressure if the final volume is 150cm\(^3\) (Assume ideality)
Parameters given:
V\(_1\) = 200 cm\(^3\); T\(_1\) = 27 + 273 = 300K.
V\(_2\) = 150 cm\(^3\); T\(_2\) = ?
P\(_2\) = 2P\(_1\).
Using the Ideal Gas Equation:
\(\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}\)
\(\frac{P_1 \times 200}{300} = \frac{2P_1 \times 150}{T_2}\)
\(\frac{2}{3} = \frac{300}{T_2}\)
T\(_2\) = 450K.
= 450K - 273K
= 177°C
177 - 27 = 150
That is the amount by which T1 must be increased.
There is an explanation video available below.
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