The Nova laser at Lawrence Livermore National Laboratory in California is used in studies of initiating
controlled nuclear fusion (Section 45.4). It can deliver a power of 1.60 × 1013 W over a time interval of 2.50
ns. Compare its energy output in one such time interval to the energy required to make a pot of tea by
warming 0.800 kg of water from 20.0°C to 100°C.
To compare the energy output of the Nova laser at Lawrence Livermore National Laboratory to the energy required to make a pot of tea, we need to calculate the energy output of the laser and the energy required to warm the water.
Let's start with calculating the energy output of the Nova laser:
Energy = Power x Time
Given that the power delivered by the laser is 1.60 × 10^13 W (watts) and the time interval is 2.50 ns (nanoseconds), we can compute the energy output:
Energy output = (1.60 × 10^13 W) x (2.50 × 10^-9 s)
= 4.00 × 10^4 J (joules)
Now, let's calculate the energy required to warm the water:
The specific heat capacity of water is 4.184 J/g°C (joules per gram per degree Celsius). To find the energy required to warm the water, we need to calculate the temperature change (∆T) and use the formula:
Energy = Mass x Specific heat capacity x ∆T
Given that the mass of water is 0.800 kg, the temperature change (∆T) is from 20.0°C to 100°C:
∆T = 100°C - 20.0°C
= 80.0°C
Energy required = (0.800 kg) x (4.184 J/g°C) x (80.0°C)
= 267.52 kJ (kilojoules)
= 2.6752 × 10^5 J (joules)
Now, we can compare the energy output of the Nova laser to the energy required to make a pot of tea:
Energy output of the laser = 4.00 × 10^4 J
Energy required for the pot of tea = 2.6752 × 10^5 J
Since the energy output of the laser is less than the energy required for making a pot of tea, we can conclude that the laser's energy output in one time interval is not sufficient to warm 0.800 kg of water from 20.0°C to 100°C.
To compare the energy output of the Nova laser to the energy required to make a pot of tea, we need to calculate the energy output of the laser and the energy required to warm the water.
1. Calculate the energy output of the Nova laser:
The power (P) is given as 1.60 × 10^13 W, and the time interval (Δt) is 2.50 ns. The formula to calculate energy (E) is E = P * Δt.
E = (1.60 × 10^13 W) * (2.50 × 10^-9 s)
E = 4.00 × 10^4 J
The energy output of the Nova laser in one time interval is 4.00 × 10^4 J.
2. Calculate the energy required to warm the water:
The specific heat capacity of water (c) is 4.186 J/g°C. The mass of water (m) is given as 0.800 kg, and the change in temperature (ΔT) is from 20.0°C to 100°C. The formula to calculate energy is E = m * c * ΔT.
E = (0.800 kg) * (4.186 J/g°C) * (100°C - 20.0°C)
E = 251.16 J/g * 0.800 kg * 80.0°C
E = 16093 J
The energy required to warm 0.800 kg of water from 20.0°C to 100°C is 16093 J.
Therefore, the energy output of the Nova laser in one time interval is much higher than the energy required to make a pot of tea.