A copper bowl and a silver bowl of equal mass were heated from 27 C to 100 C. Which required more heat? Expain. (C copper = 380 j/kg C; C silver =235 j/kg C
copper
Look at the heat capacities. Copper has a greater heat capacity per degree.
To determine which bowl required more heat, we need to calculate the amount of heat (Q) required for each bowl using the specific heat capacity formula:
Q = m * C * ΔT
Where:
Q = heat energy (in joules)
m = mass of the object (in kg)
C = specific heat capacity (in J/kg°C)
ΔT = change in temperature (in °C)
As given, both the copper and silver bowls have the same mass. Let's assume the mass to be 1 kg for simplicity.
For the copper bowl:
ΔT = (100°C - 27°C) = 73°C
Copper specific heat capacity (C) = 380 J/kg°C
m = 1 kg
Q(copper) = 1 kg * 380 J/kg°C * 73°C
Q(copper) = 27,740 J
For the silver bowl:
ΔT = (100°C - 27°C) = 73°C
Silver specific heat capacity (C) = 235 J/kg°C
m = 1 kg
Q(silver) = 1 kg * 235 J/kg°C * 73°C
Q(silver) = 17,155 J
Comparing the values, we can see that the copper bowl required more heat energy (27,740 J) compared to the silver bowl (17,155 J) to achieve the same change in temperature.
To determine which bowl required more heat to be heated from 27°C to 100°C, we need to calculate the heat energy required for each bowl separately. The heat energy is given by the equation:
Q = mcΔT
Where:
Q is the heat energy (in joules),
m is the mass of the object (in kilograms),
c is the specific heat capacity of the material (in joules per kilogram per degree Celsius), and
ΔT is the change in temperature (in degrees Celsius).
Let's calculate the heat energy for each bowl:
For the copper bowl:
Given: mass = m, c = 380 J/kg°C, and ΔT = (100°C - 27°C) = 73°C
Q(copper) = mcΔT
Q(copper) = m * 380 * 73
For the silver bowl:
Given: mass = m, c = 235 J/kg°C, and ΔT = (100°C - 27°C) = 73°C
Q(silver) = mcΔT
Q(silver) = m * 235 * 73
Now, to determine which bowl required more heat, we need to compare Q(copper) and Q(silver).
Since we are assuming that the masses of the copper and silver bowls are equal, we can cancel out the 'm' term in both equations.
Q(copper) = 380 * 73
Q(silver) = 235 * 73
Calculating the values, we find:
Q(copper) = 27740 J
Q(silver) = 17155 J
Therefore, the copper bowl required more heat (27740 J) than the silver bowl (17155 J) to be heated from 27°C to 100°C.