Two blocks of lead, one twice as heavy as the other, are both at 50 degrees Celsius. The ratio of internal energy of the heavier block to that of the lighter block is?
A)1:2
B)2:1
C)1:1
D)4:1
Its answer is option B
Because temperature and Specific heat are constant...
Hence Ratio of heat=Ratio of masses
To determine the ratio of internal energy of the heavier block to that of the lighter block, we need to understand the relationship between internal energy and temperature.
The internal energy of an object is directly proportional to its temperature. The proportionality constant is the specific heat capacity, which is unique to each substance. In other words, the internal energy (U) can be expressed as U = mcΔT, where m is the mass of the object, c is the specific heat capacity, and ΔT is the change in temperature.
Given that both blocks are at the same temperature, we can assume that their initial temperatures are the same. Since the specific heat capacity of both blocks is the same (since they are made of the same material, lead), the ratio of their internal energies would only depend on their mass.
Let's denote the mass of the lighter block as m, and the mass of the heavier block as 2m (twice as heavy as the lighter block).
So, the ratio of internal energy of the heavier block to that of the lighter block would be:
U_heavier / U_lighter = (2m)cΔT / mcΔT [canceling out the specific heat capacities and temperature change]
U_heavier / U_lighter = 2m / m
U_heavier / U_lighter = 2
Therefore, the ratio of internal energy of the heavier block to that of the lighter block is 2:1.
Hence, the correct answer is B) 2:1.