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)

A.

150°C

B.

177°C

C.

75°C

D.

120°C

Correct answer is A

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.