Calculating Signal to Noise due to thermal noise

[JoJoQuinoa]

Homework Statement

At t = 275K, the signal to noise is S/N = 15. If the system is cooled to t = 175K, what is the S/N?

Relevant Equations

Vrms = $\sqrt{2kTR\Delta f}$

The total noise from other sources and thermal is $N = N_{other} + N_{thermal}$
$N_{175}/ N_{275} = (N_{other} + \sqrt{2k(175)R\Delta f})/( N_{other} + \sqrt{2k(275)R\Delta f})$
I'm not sure how to simplify the expression as $N_{other}$ is unknown.
If I assume $N_{total} = N_{thermal}$, then
$N_{175}/ N_{275} = \sqrt{175/275} = 0.80$ meaning the thermal noise is reduced by 20% or $(S/N)_{new} = 1.20*15 = 18$.
Is this correct?

 

[Twigg]

$N_{175}/N_{275} = (N_{other} + \sqrt{2k(175)R\Delta f})/(N_{other} + \sqrt{2k(275)R\Delta f})$

What are the units of $N$, and what are the units of $\sqrt{2kTR\Delta f}$?

 

[DaveE]

If I assume Ntotal=Nthermal,

I think you have to make this assumption, unless you have more information. Suppose the signal was huge and N_other was also huge, thermal noise could be insignificant, regardless of temperature.