For each pair of substances, which of the substance with more thermal energy and explain why.
a.500 g of water at 35„aC vs. 500 g of water at 85„aC
b.500 g of water at 35„aC vs. 250 g of water at 35„aC
I don't know how to determine the answer
q = quantity of heat = mass x specific heat x T
To determine which substance has more thermal energy in each pair, we need to compare their temperatures and masses.
a. For the first pair: 500 g of water at 35ºC vs. 500 g of water at 85ºC
To compare the thermal energy, we can use the specific heat capacity formula:
Q = mcΔT
where Q represents the thermal energy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
For water, the specific heat capacity is approximately 4.18 J/(gºC).
Calculations:
1. For the first case, 500 g of water at 35ºC:
Q = (500 g)(4.18 J/(gºC))(85ºC - 35ºC) = 209,000 J
2. For the second case, 500 g of water at 85ºC:
Q = (500 g)(4.18 J/(gºC))(85ºC - 35ºC) = 209,000 J
In both cases, the thermal energy is the same, which is 209,000 J. Therefore, both substances have an equal amount of thermal energy.
b. For the second pair: 500 g of water at 35ºC vs. 250 g of water at 35ºC
Using the same formula and specific heat capacity:
1. For 500 g of water at 35ºC:
Q1 = (500 g)(4.18 J/(gºC))(35ºC - 35ºC) = 0 J (no change in temperature)
2. For 250 g of water at 35ºC:
Q2 = (250 g)(4.18 J/(gºC))(35ºC - 35ºC) = 0 J (no change in temperature)
In both cases, there is no change in temperature, so there is no transfer of thermal energy. Therefore, both substances have an equal amount of thermal energy, which is 0 J.
In conclusion, for both pairs:
- Pair a: 500 g of water at 35ºC and 500 g of water at 85ºC have an equal amount of thermal energy, which is 209,000 J.
- Pair b: 500 g of water at 35ºC and 250 g of water at 35ºC have an equal amount of thermal energy, which is 0 J (no change in temperature).