kasikiriburo no doa wo aketa totan ni, yuge ga deta.

貸切風呂 means a private bath or reserved bath.

• 貸切 = reserved for one group / privately booked
• 風呂 = bath

So this is not just any bath; it is a bath that is being used privately, such as in a hotel, inn, or hot spring facility.

The particle の connects nouns. Here it shows that ドア belongs to or is associated with 貸切風呂.

So:

• 貸切風呂のドア = the door of the private bath
• more naturally in English: the private bath door or the door to the private bath

This is one of the most common uses of の: noun + noun connection.

Because ドア is the direct object of 開けた.

• 開ける = to open something
• ドアを開けた = opened the door

The particle を marks the thing directly affected by the action.

This is the transitive/intransitive pair:

• 開ける = to open something (transitive)
• 開く = to open / be open (intransitive)

So:

• ドアを開けた = someone opened the door
• ドアが開いた = the door opened

In this sentence, a person actively opens the door, so 開けた is the correct form.

とたんに means the moment that..., just as..., or as soon as....

It connects two events that happen almost immediately one after the other.

In this sentence:

• ドアを開けたとたんに = the moment (someone) opened the door

A common nuance of とたんに is that the second event feels sudden, noticeable, or sometimes unexpected.

That is the normal grammar pattern:

• verb (past plain form) + とたん(に)

So even when the two actions happen almost at the same time, Japanese uses the past plain form before とたん.

Examples:

• 立ったとたんに = the moment I stood up
• 外に出たとたんに = the moment I went outside

So 開けたとたんに is completely standard.

No, に is often optional.

Both of these are possible:

• 開けたとたん、
• 開けたとたんに、

The version with に can sound a little more complete or slightly more formal/natural in many contexts, but the meaning is basically the same.

Because 湯気 is the subject of 出た.

• 湯気が出た = steam came out / steam appeared

Here, が marks the thing that appeared or came out.

This is different from English, where learners may want to think in terms of steam came out without noticing a subject marker. In Japanese, 湯気 is the thing performing the intransitive action 出た.

出た is the past form of 出る, which means to come out, to emerge, or to appear.

So:

• 湯気が出た literally means steam came out

In natural English, depending on context, it could also be understood as:

• steam billowed out
• steam poured out
• steam came out

Japanese 出る is a very common verb with a broad meaning, so it often sounds more general than the English translation.

Japanese often leaves obvious information unstated.

From context, the steam is understood to come out from the bath area when the door is opened. So the sentence does not need to say:

• ドアから
• 風呂場から

because the situation already makes it clear.

This is very common in Japanese: if the listener can easily infer something, it is often omitted.

Japanese often omits the subject when it is understood or unimportant.

So 開けた just means opened without explicitly saying who did it. Depending on context, it could mean:

• I opened
• he opened
• she opened
• someone opened

The focus here is not on the person, but on what happened next: steam came out immediately.

Yes.

• とき just means when
• あとで means after
• とたんに means the very moment that, with a strong sense of immediacy

Compare:

• ドアを開けたとき、湯気が出た。
  = When I opened the door, steam came out.
  This is more neutral.

• ドアを開けたとたんに、湯気が出た。
  = The moment I opened the door, steam came out.
  This emphasizes that it happened instantly.

So とたんに is a better choice if the writer wants to highlight the sudden burst of steam.

The comma helps separate the time clause from the main clause:

• 貸切風呂のドアを開けたとたんに、
• 湯気が出た。

It makes the sentence easier to read. In Japanese, commas are often used more flexibly than in English, so this comma is natural but not always absolutely required.

Yes. A useful breakdown is:

• 貸切風呂のドアを = the private bath door
• 開けた = opened
• とたんに = the moment that / as soon as
• 湯気が = steam
• 出た = came out

So the structure is:

[object] + [verb in past plain form] + とたんに + [subject] + [verb]

That pattern is worth remembering because it appears often in Japanese.