Approximately 4 x 10^9 kg of matter is converted into enery in the sun per second. Express the power output of the sun in watts.
Use the Einstein formula E = m c^2
Multiply the mass loss (per second) by c^2 to get the power output in Watts.
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To express the power output of the sun in watts, we need to use the equation:
Power = Energy / Time,
where Power is measured in watts (W), Energy is measured in joules (J), and Time is measured in seconds (s).
Given that 4 x 10^9 kg of matter is converted into energy in the sun per second, we can determine the energy by using the equation:
Energy = mass x (speed of light)^2,
where the mass is given in kilograms (kg) and the speed of light is approximately 3 x 10^8 meters per second (m/s).
So, substituting the values into the equation:
Energy = (4 x 10^9) kg x (3 x 10^8 m/s)^2.
Calculating this expression, we get:
Energy = 4 x 10^9 kg x (9 x 10^16) m^2/s^2.
Energy = (4 x 9) x (10^9 x 10^16) kg x m^2/s^2.
Energy = 36 x (10^9+16) kg x m^2/s^2.
Energy = 36 x 10^25 kg x m^2/s^2.
Now, to convert this energy into watts, we need to remember that 1 watt is equal to 1 joule per second. So, we divide the energy by the time:
Power = (36 x 10^25) J / 1 s.
Multiplying and dividing the expression by 1, we find:
Power = 36 x 10^25 J/s.
Therefore, the power output of the sun is approximately 36 x 10^25 watts (W).