I've seen often in movies an astronaut exposed to the void (i.e. his helmet broken) and the depiction is him freezing nearly instantly. Considering that in void radiation is the only way a body may transfer heat outside it may seem a bit surprising. I suppose this is what it happens but I wonder how fast this really occurs.

To put a simpler case, let's imagine a 1 liter sphere filled with water and uniformly heated at 323.15 K (50 C) left in outer space at 3 K. Do not consider the sphere surface. How many time will it take to cool down to 3 K?

Edit: This problem is well beyond my knowledge of physics and maths, I'm a bit old but still curious. I said not to consider surface just to make it simpler but if necessary then do it. My goal is to understand if radiation can cool down a body so fast as it is depicted un movies.

Edit: As per comment received let's consider a final temperature of 5 K so it doesn't take infinite time to reach it.

I've seen often in movies an astronaut exposed to vacuum (i.e. his helmet broken) and the depiction is him freezing nearly instantly. Considering that in vacuum radiation is the only way a body may transfer heat outside it may seem a bit surprising. I suppose this is what it happens but I wonder how fast this really occurs.

To put a simpler case, let's imagine a 1 liter sphere filled with water and uniformly heated at 323.15 K (50 C) left in outer space at 3 K. Do not consider the sphere surface. How many time will it take to cool down to 3 K?

Edit: This problem is well beyond my knowledge of physics and maths, I'm a bit old but still curious. I said not to consider surface just to make it simpler but if necessary then do it. My goal is to understand if radiation can cool down a body so fast as it is depicted un movies.

Edit: As per comment received let's consider a final temperature of 5 K so it doesn't take infinite time to reach it.

I've seen often in movies an astronaut exposed to the void (i.e. his helmet broken) and the depiction is him freezing nearly instantly. Considering that in void radiation is the only way a body may transfer heat outside it may seem a bit surprising. I suppose this is what it happens but I wonder how fast this really occurs.

To put a simpler case, let's imagine a 1 liter sphere filled with water and uniformly heated at 323.15 K (50 C) left in outer space at 3 K. Do not consider the sphere surface. How many time will it take to cool down to 3 K?

Edit: This problem is well beyond my knowledge of physics and maths, I'm a bit old but still curious. I said not to consider surface just to make it simpler but if necessary then do it. My goal is to understand if radiation can cool down a body so fast as it is depicted un movies.

I've seen often in movies an astronaut exposed to the void (i.e. his helmet broken) and the depiction is him freezing nearly instantly. Considering that in void radiation is the only way a body may transfer heat outside it may seem a bit surprising. I suppose this is what it happens but I wonder how fast this really occurs.

To put a simpler case, let's imagine a 1 liter sphere filled with water and uniformly heated at 323.15 K (50 C) left in outer space at 3 K. Do not consider the sphere surface. How many time will it take to cool down to 3 K?

Edit: This problem is well beyond my knowledge of physics and maths, I'm a bit old but still curious. I said not to consider surface just to make it simpler but if necessary then do it. My goal is to understand if radiation can cool down a body so fast as it is depicted un movies.

Edit: As per comment received let's consider a final temperature of 5 K so it doesn't take infinite time to reach it.

I've seen often in movies an astronaut exposed to the void (i.e. his helmet broken) and the depiction is him freezing nearly instantly. Considering that in void radiation is the only way a body may transfer heat outside it may seem a bit surprising. I suppose this is what it happens but I wonder how fast this really occurs.

To put a simpler case, let's imagine a 1 liter sphere filled with water and uniformly heated at 323.15 K (50 C) left in outer space at 3 K. Do not consider the sphere surface. How many time will it take to cool down to 3 K?

I've seen often in movies an astronaut exposed to the void (i.e. his helmet broken) and the depiction is him freezing nearly instantly. Considering that in void radiation is the only way a body may transfer heat outside it may seem a bit surprising. I suppose this is what it happens but I wonder how fast this really occurs.

To put a simpler case, let's imagine a 1 liter sphere filled with water and uniformly heated at 323.15 K (50 C) left in outer space at 3 K. Do not consider the sphere surface. How many time will it take to cool down to 3 K?

Edit: This problem is well beyond my knowledge of physics and maths, I'm a bit old but still curious. I said not to consider surface just to make it simpler but if necessary then do it. My goal is to understand if radiation can cool down a body so fast as it is depicted un movies.