Two lead spheres at the same temperature have radii in the ratio 1:2.what is the ratio of their heat capacities
SVTP=SVTP
GIVEN TEMPERATURE IS SAME
SVP=SVP
DENSITY IS SAME BECOZ OF SAME MATERIAL
S1V1=S2V2
V=R3
THEREFORE
S1(R1)3=S2(R2)3
S1 (1)= S2(8)
S1/S2=8/1
S1:S2=8:1
heat capacity is proportional to mass
mass is proportional to volume
volume is proportional to the cube of the radius
heat cap. ratio is ... 1³:2³
super mama
To determine the ratio of the heat capacities of two lead spheres, we need to consider the relationship between heat capacity, volume, and temperature. The formula for heat capacity is given by:
C = m * Cp
Where:
C is the heat capacity,
m is the mass of the object, and
Cp is the specific heat capacity of the material.
In this case, we have two lead spheres at the same temperature. Since the temperature is the same, we can ignore it. The heat capacity will depend on the mass and specific heat capacity.
The mass of a sphere can be calculated using the formula for the volume of a sphere:
V = (4/3) * π * r³
Where:
V is the volume of the sphere, and
r is the radius of the sphere.
Since the radii of the two spheres are in a 1:2 ratio, let's assume the radii are x and 2x, respectively.
The volume of the first sphere is V₁ = (4/3) * π * x³
The volume of the second sphere is V₂ = (4/3) * π * (2x)³ = (4/3) * π * 8x³ = 32 * (4/3) * π * x³ = 32 * V₁
Thus, the ratio of the volumes is: V₁ : V₂ = 1 : 32.
Now, since the density of lead is the same for both spheres, and density is defined as mass divided by volume, we can say that the ratio of their masses is also 1 : 32.
Finally, the ratio of the heat capacities (C₁ : C₂) will be equal to the ratio of the masses (m₁ : m₂), because the specific heat capacity is the same for both spheres:
Heat capacity ratio: C₁ : C₂ = m₁ : m₂ = 1 : 32
Therefore, the ratio of the heat capacities of the two lead spheres is 1 : 32.