Heat is added to a silver bar of mass 0.034 kg and length 0.28 m. The bar expands by an amount of 3.8×10-4 m. How much heat was added?
Please i need the answer and the equation to get to the answer Thanks!
To solve this problem, we can use the equation for linear thermal expansion:
∆L = αL∆T
Where:
∆L is the change in length of the bar
α is the coefficient of linear expansion of the material (which is given for silver)
L is the original length of the bar
∆T is the change in temperature
In this case, we are given the change in length (∆L = 3.8×10^(-4) m), the original length (L = 0.28 m), and the coefficient of linear expansion for silver (which is typically around 0.000019 m/°C). However, we are not given the change in temperature (∆T).
Since the equation involves both ∆L and ∆T, we need to rearrange it to solve for ∆T:
∆T = ∆L / (αL)
Plugging in the known values, we have:
∆T = (3.8×10^-4 m) / (0.000019 m/°C) = 20 °C
Therefore, the change in temperature (∆T) is 20 °C.
Now, we can use the equation for heat (Q) to find the amount of heat added:
Q = mc∆T
Where:
Q is the amount of heat added
m is the mass of the bar
c is the specific heat capacity of the material (which is specific to each material)
∆T is the change in temperature
In this case, we are given the mass of the bar (m = 0.034 kg) and the change in temperature (∆T = 20 °C). However, we are not given the specific heat capacity (c) of silver.
Without the specific heat capacity, we cannot determine the amount of heat added accurately. The specific heat capacity is a property of the material and varies for different substances.
In conclusion, we can calculate the change in temperature (∆T) using the coefficient of linear expansion, but to determine the amount of heat added (Q), we also need the specific heat capacity of silver.