a) When a material is heated, the change in temperature of the material for any given amount of energy is dependent on the material’ s heat capacity. How much energy will water requirements for each 1C increase in temperature?
b) On average, 1370 W of radiation heat energy is incident on 1m2 of Earth's surface from the Sun every second. Assuming 100% efficient and no energy losses, how long would it take for the Sun to heat 1 litre of water by 1oC using 1m2 of heat-absorbing material?
a) Q=mc(t1-t2)
a) The amount of energy required to increase the temperature of a material by 1°C is determined by its specific heat capacity. The specific heat capacity of water is approximately 4.186 J/g·°C.
To calculate the energy required to heat water by 1°C, we need to know the mass of the water. Let's assume we have 1 gram of water.
The formula to calculate the energy (Q) is Q = m * c * ΔT, where:
- Q is the energy in joules
- m is the mass of the water in grams
- c is the specific heat capacity of water in J/g·°C
- ΔT is the change in temperature in degrees Celsius
Therefore, for 1 gram of water, the energy required to heat it by 1°C would be:
Q = 1 g * 4.186 J/g·°C * 1°C = 4.186 Joules
Note: If you have a different mass of water, simply multiply the mass in grams by the specific heat capacity to calculate the energy needed.
b) Since we know the power of radiation incident on 1m² of Earth's surface every second, we can calculate the total energy received per second. The unit for power is Watts (W), which is equivalent to Joules per second (J/s).
Given the power of 1370 W (J/s) and assuming 100% efficiency and no energy losses, the energy received per second will be 1370 J.
To determine the time required for the Sun to heat 1 litre (1000 grams) of water by 1°C, we can use the formula from part a. However, we need to convert the energy received per second to the energy required to heat 1000 grams of water by 1°C.
Energy required = 1000 g * 4.186 J/g·°C = 4186 J
Now we can calculate the time (t) by dividing the total energy required by the energy received per second:
t = energy required / energy received per second
t = 4186 J / 1370 J/s ≈ 3.06 seconds
Therefore, assuming 100% efficiency and no energy losses, it would take approximately 3.06 seconds for the Sun to heat 1 litre of water by 1°C using 1m² of heat-absorbing material.