While polishing a 1-kg brass statue, you do 760 J of work against sliding friction. Assuming that all of the resulting heat flows into the statue, how much does its temperature rise?
Q=c•m•ΔT
For brass c= 385 J/kg•K
ΔT= Q/c•m=760/385•1=1.97º
Thank you Elena.
To find out how much the temperature of the brass statue rises, we need to use the specific heat capacity of brass. The specific heat capacity is the amount of heat energy required to raise the temperature of a given mass of a substance by one degree Celsius.
First, let's recall the formula to calculate the change in temperature of an object:
Q = mcΔT
Where:
Q = amount of heat energy transferred to the object (in joules)
m = mass of the object (in kilograms)
c = specific heat capacity of the material (in joules per kilogram per degree Celsius)
ΔT = change in temperature (in degrees Celsius)
In this case, the mass of the brass statue is given as 1 kg, and the amount of work done against sliding friction is given as 760 J. We assume all of the resulting heat flows into the statue, so Q is equal to 760 J.
Next, we need to find the specific heat capacity of brass. The specific heat capacity varies slightly depending on the composition of the brass, but it is typically around 385 J/kg°C.
Now we can rearrange the formula to solve for ΔT:
ΔT = Q / (mc)
Substituting the given values, we have:
ΔT = 760 J / (1 kg * 385 J/kg°C)
Simplifying this equation, we find:
ΔT = 760 / 385 ≈ 1.97°C
Therefore, the temperature of the brass statue will rise by approximately 1.97 degrees Celsius when 760 J of work is done against sliding friction.