PLEASE HELP ME!!!!!
Which requires more energy? Heating up a 350 mL cup of coffee from 25C to 65C? or Warming the surface of a Lake (2,000,000,000 mL) from 28C to 29C.
and Prove your answer.
To determine which task requires more energy, we need to calculate the amount of heat transferred in each scenario using the formula: Q = mcΔT.
For the first scenario, heating up a 350 mL cup of coffee from 25C to 65C, we can use the following values:
- Mass (m) = 350 g (since the density of water is close to 1 g/mL)
- Specific heat capacity (c) = 4.18 J/g°C (specific to water)
- Change in temperature (ΔT) = 65°C - 25°C = 40°C
By plugging these values into the formula, we get:
Q1 = 350 g × 4.18 J/g°C × 40°C = 58,520 J
Now, let's calculate the amount of energy required for warming the surface of a lake from 28°C to 29°C. We'll assume the specific heat capacity of water for simplicity.
- Mass (m) = 2,000,000,000 g (since 1 mL of water is equivalent to 1 g)
- Specific heat capacity (c) = 4.18 J/g°C (specific to water)
- Change in temperature (ΔT) = 29°C - 28°C = 1°C
Plugging these values into the formula:
Q2 = 2,000,000,000 g × 4.18 J/g°C × 1°C = 8,360,000,000 J
Comparing the two values, Q1 (58,520 J) for heating up the cup of coffee and Q2 (8,360,000,000 J) for warming the lake's surface, we can clearly see that warming the lake requires significantly more energy.
Therefore, warming the surface of a lake (2,000,000,000 mL) from 28°C to 29°C requires more energy than heating up a 350 mL cup of coffee from 25°C to 65°C.