Two objects A and B have the same mass and the same specific heat. Object A is heated from 30°C to 70°C and object B is cooled from 70°C to 30°C. How are the thermal energies of the two objects related after the temperature change has occurred?
A. The thermal energies of A and B have the same magnitude but opposite signs.
B. The thermal energies of A and B are the same.
C. The thermal energy of B is higher than the thermal energy of A.
D. The thermal energy of A is 40 kJ and the thermal energy of B is 30 kJ.
answer is a
Its A
The thermal energy of an object is given by the equation Q = mcΔT, where Q is the thermal energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.
In this case, objects A and B have the same mass and the same specific heat. Therefore, the thermal energy of an object is directly proportional to the change in temperature.
Object A is heated from 30°C to 70°C, resulting in a change in temperature of ΔT = 70°C - 30°C = 40°C.
Object B is cooled from 70°C to 30°C, resulting in a change in temperature of ΔT = 30°C - 70°C = -40°C.
Since the thermal energy is directly proportional to the change in temperature, the thermal energy of object A will be the same magnitude as the thermal energy of object B, but with opposite signs.
Therefore, the correct answer is:
A. The thermal energies of A and B have the same magnitude but opposite signs.
To answer this question, we need to understand the relationship between thermal energy, mass, specific heat, and temperature change.
Thermal energy (Q) is directly proportional to both the mass (m) and the change in temperature (ΔT) of an object. The equation to calculate thermal energy is Q = m * c * ΔT, where c is the specific heat.
In this case, objects A and B have the same mass and the same specific heat. So, the only difference between them is the temperature change.
Object A is heated from 30°C to 70°C, resulting in a temperature change of ΔT = 70°C - 30°C = 40°C.
Object B is cooled from 70°C to 30°C, resulting in a temperature change of ΔT = 30°C - 70°C = -40°C (note the negative sign indicating a decrease in temperature).
Now, let's compare the thermal energies of A and B:
For object A: Q = m * c * ΔT = m * c * 40°C
For object B: Q = m * c * ΔT = m * c * (-40°C) = -m * c * 40°C (note the negative sign indicating a negative thermal energy)
Comparing the two equations, we see that the thermal energies of A and B have the same magnitude (m * c * 40°C) but opposite signs. This means that option A is the correct answer:
A. The thermal energies of A and B have the same magnitude but opposite signs.