how much mass is converted to energy per day ina nuclear power plant operated at a level of 100 megawatts?
To calculate the mass converted to energy per day in a nuclear power plant, we need to use Einstein's famous equation, E=mc^2, which relates energy (E), mass (m), and the speed of light (c).
First, we need to convert the power output from megawatts (MW) to watts (W). 1 megawatt = 1,000,000 watts. So, 100 megawatts = 100,000,000 watts.
Next, we need to determine the amount of energy produced per day. Since power is the rate at which energy is generated or consumed, we can multiply the power output by the amount of time in a day. Let's assume a day has 24 hours.
Energy produced per day = Power output × Time
= 100,000,000 W × 24 hours
= 2,400,000,000 watt-hours (Wh)
Now, we need to convert the energy from watt-hours to joules, as E=mc^2 uses joules as the unit of energy.
1 watt-hour (Wh) = 3600 joules (J)
Energy produced per day in joules = 2,400,000,000 Wh × 3600 J/Wh
= 8,640,000,000,000 J
Using Einstein's equation, we know that the energy (E) is equal to the mass (m) multiplied by the speed of light squared (c^2). Rearranging the formula, we get:
m = E / c^2
Let's assume the speed of light, c, is approximately 3 × 10^8 meters per second (m/s).
Mass converted to energy per day = Energy produced per day / (c^2)
= 8,640,000,000,000 J / (3 × 10^8 m/s)^2
= 8,640,000,000,000 J / 9 × 10^16 m^2/s^2
Simplifying further, we get:
Mass converted to energy per day ≈ 9.6 × 10^-8 kg
Therefore, approximately 9.6 × 10^-8 kilograms of mass would be converted to energy per day in a nuclear power plant operated at a level of 100 megawatts.
To determine how much mass is converted to energy per day in a nuclear power plant, we can use Einstein's famous equation, E=mc², which states that energy (E) is equal to mass (m) multiplied by the speed of light (c) squared.
Given that the power output of the nuclear power plant is 100 megawatts, we need to convert this into energy. One megawatt is equal to one million joules per second. Therefore, 100 megawatts is equal to 100 million joules per second.
Next, we need to convert the energy output into mass. Since the equation E=mc² relates energy to mass, we can rearrange it to solve for mass (m), which becomes m = E/c².
The speed of light (c) is approximately 3 x 10⁸ meters per second. Now, substitute the energy (E) of 100 million joules per second and the speed of light (c) into the equation:
m = (100 million joules per second) / (3 x 10⁸ meters per second)²
Calculate the value:
m = 100,000,000 / (9 x 10¹⁶)
m ≈ 1.11 x 10⁻⁷ kilograms (or 111 micrograms)
Therefore, in a nuclear power plant operating at a level of 100 megawatts, approximately 1.11 x 10⁻⁷ kilograms (or 111 micrograms) of mass are converted to energy per day.
100 MJ/s
e = m c^2 ... 1E8 = m * (3E8)^2
m = 1.1E-9 kg
multiply by seconds in a day