Multiple-Concept Example 11 deals with a situation that is similar, but not identical, to that here. When 4620 J of heat are added to a 0.194-m-long silver bar, its length increases by 6.14 x 10-3 m. What is the mass of the bar?
To find the mass of the silver bar, we can use the formula:
mass = (heat)/(specific heat capacity x change in temperature)
However, in this case, we are given the length change of the bar, not the change in temperature. So, we need to find the change in temperature first.
Using Multiple-Concept Example 11, we know that:
heat = mass x specific heat capacity x change in temperature
In that example, a similar situation was given where heat, length change, and original length were known. By rearranging the formula, we can solve for change in temperature.
change in temperature = heat / (mass x specific heat capacity)
Now, let's calculate the change in temperature using the given values:
heat = 4620 J
length change = 6.14 x 10^(-3) m
original length = 0.194 m
specific heat capacity for silver = 0.24 J/(g°C) (given or known value)
change in temperature = heat / (mass x specific heat capacity)
change in temperature = 4620 J / (mass x 0.24 J/(g°C))
To proceed further, we need to convert the units of length change and mass to match the units of the specific heat capacity. The specific heat capacity is given in J/(g°C), so we need to convert the length change to grams.
To convert the length change to grams, we can use the density of silver. The density of silver is typically around 10.5 g/cm³.
mass = density x volume
mass = density x (original length + length change) x cross-sectional area
Cross-sectional area = width x height = (assuming a rectangular bar) = constant for a given bar
Let's say the width and height of the bar are w and h respectively, then:
cross-sectional area = w x h
Now, let's substitute the values into the equations and calculate the mass:
cross-sectional area = w x h (constant)
change in temperature = 4620 J / (mass x 0.24 J/(g°C))
mass = density x (original length + length change) x cross-sectional area
It is not possible for us to give exact values in this explanation as we don't have the cross-sectional area and the width and height of the bar. You need to substitute the appropriate values in the equations and solve for mass using these values.