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Ideal Gas Equation

A large cylin...

Question

A large cylindrical tank contains $0.750 m^{3}$ of nitrogen gas at $27^{\circ} C$ and $1.50 \times 10^{5}$ Pa (absolute pressure). The tank has a tight fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to $0.480 m^{3}$ and the temperature is increased to $157^{\circ} C$

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Solution

From the ideal gas equation $P V = n R T$ , since the number of moles have to remains constant,

$\frac{P V}{T}$ must be constant.

Hence, $\frac{(1.5 X 10^{5}) (0.75)}{300} = \frac{P (0.48)}{430}$

$P = \frac{43}{30} 11.25 X 10^{5} P a = 3.36 X 10^{5} P a$

Answer is $3.36 X 10^{5} P a$

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