A 23-m 3 tank is filled with 1570 moles of an ideal gas. The temperature of the

Question

A 23-m3 tank is filled with 1570 moles of an ideal gas. The temperature of the gas is initially 295 K, but it is raised to 718 K.

Let's assume that the tank is made out of a material which has a coefficient of linear expansion of 6.5 × 10-5 K-1, and that the temperature of the tank is always the same as the temperature of the gas. Remember that the space inside the tank will expand as if it were made of the material surrounding it.

1) Given that the tank expands a bit, what is the actual change in the gas pressure due to the increase in temperature?

Explanation / Answer

Volume of tank at 718 K, V = 23*(1+ 6.5 × 10-5(718-295)) =23.632 m3

Now from ideal gas equation

PV = nRT

P1 =nRT1/V1  = 1570*(8.314 J / mol. K)*295 K/23 m3

= 167418.66 Pa

P2 =nRT2/V2 = 1570*(8.314 J / mol. K)*718 K/23.632 m3

= 396576.124 Pa

P2 - P1= 229157.47 Pa =2.3 Atm. Pressure

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