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By what amount must the temperature of 200cm $^3$ of Nitrog...

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

View answer & explanation

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.

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