How Long Would the Sun Last if it Burned Like a Quasar?

[Jimmy87]

Homework Statement

Quasars have a luminosity on the order of 10^12 times more than our Sun. Our Sun is expected to last 5 billion years. Using this number estimate (in seconds) how long our Sun would last if it started using energy at the rate of a Quasar.

Homework Equations

None

The Attempt at a Solution

From the information given, there is no equation given so I did some research and it looks like you can roughly approximate that the luminosity of a star is inversely proportional to its lifetime therefore I did the following:

5 billion years = 1.58 x 10^17 seconds

I then simply divided this by 10^12 to give - 158,000 s or 44 hours

Does this sound right? Also, is it acceptable to approximate the age of a star to being inversely proportional to its luminosity. I see no other way of doing it based on the information given.

Thanks.

 

[gneill]

Looks reasonable. The underlying assumption is that there is a fixed amount of energy available and that the "burn" rate (power output) is constant over the lifetime of the object.

 

[Jimmy87]

Looks reasonable. The underlying assumption is that there is a fixed amount of energy available and that the "burn" rate (power output) is constant over the lifetime of the object.

Thanks. I just found out that nuclear fusion in a quasar can convert a set amount of mass into energy to an order of magnitude of 20 times more than mass into energy in a normal star. How would my answer change? Would it just be 20 times longer i.e. 880 hours?

 

[gneill]

Thanks. I just found out that nuclear fusion in a quasar can convert a set amount of mass into energy to an order of magnitude of 20 times more than mass into energy in a normal star. How would my answer change? Would it just be 20 times longer i.e. 880 hours?

I don't see how your answer to the problem would change, because it doesn't depend upon the mass. You were given relative energy production rates only. There was nothing in your original problem statement to suggest that the total available energy should be modified.

On the other hand, if this is a new question where you are to consider that the total energy available changes due to different nuclear processes coming into play under different operating conditions, then yes, you'd have to take that into account.

 

[Jimmy87]

I don't see how your answer to the problem would change, because it doesn't depend upon the mass. You were given relative energy production rates only. There was nothing in your original problem statement to suggest that the total available energy should be modified.

On the other hand, if this is a new question where you are to consider that the total energy available changes due to different nuclear processes coming into play under different operating conditions, then yes, you'd have to take that into account.

Thanks for the answer. So if a new question was considered, e.g.

Quasars have a luminosity on the order of 10^12 times more than our Sun. Our Sun is expected to last 5 billion years. Using this number estimate (in seconds) how long our Sun would last if it started using energy at the rate of a Quasar. You need to take into account that the nuclear processes that operate inside Quasars are 20 times more efficient i.e. there is 20 times more energy converted per kg of mass compared to stars.

In this case would you simply multiply the previous answer by 20, therefore giving 880 hours. More logic is that the efficiency will slightly offset the reduced aging caused by the increased luminosity. For example, in a hypothetical situation you could have a star that is 20 times more luminous but 20 times more efficient which would result in no loss of lifetime. At least that's my interpretation of the situation?

 

[gneill]

Thanks for the answer. So if a new question was considered, e.g.

Quasars have a luminosity on the order of 10^12 times more than our Sun. Our Sun is expected to last 5 billion years. Using this number estimate (in seconds) how long our Sun would last if it started using energy at the rate of a Quasar. You need to take into account that the nuclear processes that operate inside Quasars are 20 times more efficient i.e. there is 20 times more energy converted per kg of mass compared to stars.

In this case would you simply multiply the previous answer by 20, therefore giving 880 hours. More logic is that the efficiency will slightly offset the reduced aging caused by the increased luminosity. For example, in a hypothetical situation you could have a star that is 20 times more luminous but 20 times more efficient which would result in no loss of lifetime. At least that's my interpretation of the situation?

Sounds reasonable.