## Example: Ideal Gas Law – Gas compression inside a pressurizer

**Pressure in the primary circuit** of PWRs is maintained by a **pressurizer**, a separate vessel that is connected to the primary circuit (hot leg) and partially filled with water which is heated to the **saturation temperature** (boiling point) for the desired pressure by submerged **electrical heaters**. During the plant heatup the pressurizer can be filled by nitrogen instead of saturated steam.

Assume that a pressurizer contains **12 m**** ^{3}** of nitrogen at

**20°C**and

**15 bar**. The temperature is raised to

**35°C**, and the volume is reduced to

**8.5 m**

**. What is the final pressure of the gas inside the pressurizer? Assume that the gas is ideal.**

^{3}**Solution:**

Since the gas is ideal,we can use the ideal gas law to relate its parameters, both in the **initial state i **and in the **final state f**. Therefore:

*p _{init}V_{init} = nRT_{init}*

and

*p _{final}V_{final} = nRT_{final}*

Dividing the second equation by the first equation and solving for ** p_{f}** we obtain:

*p _{final} = p_{init}T_{final}V_{init} / T_{init}V_{final}*

Note that we cannot convert units of volume and pressure to basic SI units, because they cancel out each other. On the other hand we have to use Kelvins instead of degrees of Celsius. Therefore T_{init} = 293 K and T_{final} = 308 K.

It follows, the resulting pressure in the final state will be:

* p _{final} *

*= (15 bar) x (308 K) x (12 m*

^{3}) / (293 K) x (8.5 m^{3}*) =*

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