Which object in the following pair has greater total internal energy, assuming both objects in the pair are in thermal equilibrium?
a 1kg block of ice at -25 degrees Celsius or seven 12g ice cubes at -25 degrees Celsius
the 1kg of ice has much more thermal capacity.
To determine which object has greater total internal energy, we need to calculate the internal energy of each object.
The internal energy of an object can be calculated using the equation:
Internal Energy (U) = mass (m) * specific heat capacity (c) * change in temperature (ΔT)
First, let's calculate the internal energy of the 1kg block of ice at -25 degrees Celsius.
Mass (m) = 1kg
Specific heat capacity (c) of ice = 2.09 J/g°C
Change in temperature (ΔT) = final temperature - initial temperature
As the final temperature is not given, we can assume that the block of ice is still at -25 degrees Celsius. Therefore, the change in temperature (ΔT) is 0.
Internal Energy (U) = 1kg * 2.09 J/g°C * 0°C = 0 J
Next, let's calculate the internal energy of the seven 12g ice cubes at -25 degrees Celsius.
Mass (m) of each ice cube = 12g
Total mass of the seven ice cubes = 12g * 7 = 84g = 0.084kg
Specific heat capacity (c) of ice = 2.09 J/g°C
Change in temperature (ΔT) = 0°C
Internal Energy (U) = 0.084kg * 2.09 J/g°C * 0°C = 0 J
As we can see, the internal energy of both objects is 0 J since the change in temperature is 0. Therefore, both objects have the same total internal energy.
Please note that at thermal equilibrium, the total internal energy of the objects will be the same regardless of the size or number of objects, as long as their temperatures are the same.