The average temperature of the present universe is 2.7 K. What was the cosmic scale factor of the universe when the average temperature was 270 K?
Question
The average temperature of the present universe is 2.7 K. What was the cosmic scale factor of the universe when the average temperature was 270 K?
Solution
The cosmic scale factor of the universe is inversely proportional to the temperature of the universe. This means that if the temperature of the universe increases, the cosmic scale factor decreases and vice versa.
Given that the average temperature of the present universe is 2.7 K and the cosmic scale factor is 1 (by definition), we can use these values to find the cosmic scale factor when the average temperature was 270 K.
The relationship between the temperature and the cosmic scale factor is given by:
T1 / T2 = a2 / a1
where:
- T1 is the temperature of the universe at time 1 (2.7 K in this case)
- T2 is the temperature of the universe at time 2 (270 K in this case)
- a1 is the cosmic scale factor at time 1 (1 in this case)
- a2 is the cosmic scale factor at time 2 (what we're trying to find)
Plugging in the given values, we get:
2.7 K / 270 K = 1 / a2
Solving for a2, we find that a2 = 2.7 K / 270 K = 0.01.
So, the cosmic scale factor of the universe when the average temperature was 270 K was 0.01.
Similar Questions
The photons in the CMB were emitted when the universe was about 1/1100 of its current size. What was the temperature of the universe at that time? (The present day temperature of the CMB is 2.7 K.)
What is the temperature of the Cosmic Microwave Background (CMB)?Group of answer choices70 Farenheit0 Celsius100 Kelvin3 Kelvin
When the light from a distant galaxy is analysed, it is found that a line on its spectrum is 32 nm longer than when the same spectrum is produced on Earth. Given that the light was emitted with a wavelength of 430 nm, calculate the cosmic scale factor when it was emitted. Give your answer to 2 significant figures.
If the Hubble constant was measured to be 5% higher than its current value, by what factor would the value of critical density of the universe change? Give your answer as a percentage correct to one significant figure.
uppose that the Hubble constant had a value of H = 120 km/s/Mpc. What would be the age of the universe? billion yearsWhat if H had a value of 30 km/s/Mpc? billion years
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.