Die Röstgase verschwinden in der Abkühlphase.

Because Röstgase is plural. The singular form is das Röstgas.

• das Röstgas = the roasting gas / roast gas
• die Röstgase = the roasting gases / fumes

Since the noun is plural here, the article is die. German uses die for all nominative plural nouns, regardless of gender in the singular.

A singular version of the sentence would be:

Das Röstgas verschwindet in der Abkühlphase.

Because the subject die Röstgase is plural.

In the present tense, verschwinden is conjugated like this:

• ich verschwinde
• du verschwindest
• er/sie/es verschwindet
• wir verschwinden
• ihr verschwindet
• sie/Sie verschwinden

Since die Röstgase is a they subject, the correct verb form is verschwinden.

So:

• Das Röstgas verschwindet = singular
• Die Röstgase verschwinden = plural

Because in is a two-way preposition in German: it can take either accusative or dative, depending on the meaning.

• accusative: movement/change toward something
• dative: location or situation within something

Here, in der Abkühlphase does not describe movement into a place. It describes what happens during that phase. So German uses the dative.

That is why you get:

• die Abkühlphase = nominative
• in der Abkühlphase = dative

Here it expresses time, not physical location.

German often uses in + dative to mean something like:

• during
• in the course of
• within

So in der Abkühlphase is best understood as:

during the cooling phase

Even though in often means in physically, it can also be used for time periods like this.

Because Abkühlphase is a feminine noun: die Abkühlphase.

When a feminine noun is in the dative singular, the definite article changes:

• nominative: die Abkühlphase
• dative: der Abkühlphase

So der here does not mean the noun is masculine. It is simply the dative form of the feminine article die.

German very often combines words into compound nouns.

Röstgase

This is made from:

• Röst- = roasting-related
• Gase = gases

The most important part is the last part, because it tells you the basic meaning and grammar. Since the last part is Gase, the whole word is plural.

Abkühlphase

This is made from:

• Abkühl- = cooling / cooling-down
• Phase = phase

Again, the last part controls the grammar. Since Phase is feminine (die Phase), the whole compound is also feminine:

die Abkühlphase

This is a very common pattern in German.

Yes. That is completely correct.

German main clauses follow the verb-second rule. That means the finite verb must stay in the second position, but the first element can change.

So both of these are correct:

• Die Röstgase verschwinden in der Abkühlphase.
• In der Abkühlphase verschwinden die Röstgase.

The difference is mostly emphasis:

• starting with Die Röstgase focuses first on the gases
• starting with In der Abkühlphase focuses first on the time frame

Not always in a dramatic or magical sense. Verschwinden often simply means that something is no longer present, goes away, or ceases to be noticeable.

Depending on context, English might translate it as:

• disappear
• vanish
• dissipate
• die away
• be gone

So in a technical or scientific context, verschwinden can sound perfectly natural even if English would prefer a more specific verb.

Because in German, all nouns are capitalized.

So:

• Röstgase is a noun
• Abkühlphase is a noun

That is why both start with capital letters. This is a basic rule of German spelling and is one of the biggest differences from English.