Esta sala serve para estudar em silêncio.

Because sala is a feminine singular noun, so the demonstrative has to match it:

• esta sala = this room
• este quarto = this bedroom/room

So esta agrees with sala in gender and number.

In European Portuguese, the demonstratives usually work like this:

• esta = this, near the speaker
• essa = that, near the listener or already mentioned
• aquela = that over there, farther away

So esta sala means this room. In real conversation, native speakers do not always follow the distance distinction perfectly, but this is the basic system learners should know.

Sala is a general word for a room or hall. Depending on context, it can mean things like:

• living room
• classroom
• waiting room
• study room

In this sentence, it just means a room intended for studying. English often needs a more specific word, but Portuguese can stay broader.

The verb servir can mean to serve, but in the pattern servir para + infinitive/noun, it means:

• to be for
• to be used for
• to be intended for

So Esta sala serve para estudar em silêncio means that the room’s purpose or function is studying quietly.

Yes, that is also natural.

The difference is small:

• serve para estudar = emphasizes the function or use
• é para estudar = emphasizes what it is meant for

Both are good Portuguese. Serve para sounds slightly more like is used for.

Because after para to express purpose, Portuguese normally uses the infinitive:

• para estudar = to study / for studying
• para ler = to read / for reading
• para trabalhar = to work / for working

So serve para estudar literally means serves for studying or more naturally is for studying.

Because estudar here is a verb, not a noun.

In para estudar, estudar is the infinitive form to study. Portuguese commonly uses para + infinitive directly to express purpose, with no article needed.

Em silêncio literally means in silence, and it is a very common, natural way to say:

• silently
• quietly
• without talking

You could say silenciosamente, but that often sounds more formal, literary, or less natural in everyday speech. In this sentence, em silêncio is the more idiomatic choice.

Because em silêncio is a fixed expression meaning in silence or silently.

• em silêncio = silently / in silence
• no silêncio = in the silence, usually referring to a particular silence or quiet atmosphere

So here, em silêncio describes how people study, not a specific silence as a thing.

Because Portuguese usually does not need an extra subject pronoun when the subject is already clear.

Here the subject is already stated:

• Esta sala serve...

Adding ela would usually sound unnecessary:

• Esta sala ela serve... → not natural in standard usage here

Portuguese often leaves pronouns out when the noun or verb already makes the subject clear.

A rough European Portuguese pronunciation would be something like:

ESH-tuh SAH-luh SEHR-v(uh) puh-ruh esh-too-DAR ẽ see-LEN-syu

A few helpful points:

• esta often sounds like eshta
• final unstressed vowels are reduced in Portugal
• em sounds nasal
• silêncio has stress on lên

This is only an approximation for English speakers, but it helps you hear the overall shape of the sentence.