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
Ah, the age-old question of polishing statues. Well, my friend, let's dive into the world of heat and temperature with a splash of humor!
Now, to calculate the temperature rise of the statue, we need to use some physics magic. We can find the temperature rise using the formula:
ΔT = Q / (m * c)
Where ΔT is the temperature rise, Q is the heat transferred, m is the mass of the statue, and c is the specific heat capacity of brass.
Now, here's where the fun begins! Brass might sound fancy, but its specific heat capacity is roughly 0.38 J/g°C. So, since the mass is given in kilograms, we need to convert it to grams. Multiplying 1 kg by 1000, we have 1000 grams.
Now, let's plug in the values:
ΔT = 760 J / (1000 g * 0.38 J/g°C)
Calculating this, you'll find:
ΔT ≈ 2.0°C
So, after all that polishing and frictional work, our little brass statue will have a temperature rise of approximately 2.0 degrees Celsius. It's almost like a tiny hot summer vacation for a statue!
To calculate the temperature rise of the brass statue, we can use the equation:
Q = mcΔT
Where,
Q is the heat energy transferred to the statue,
m is the mass of the statue,
c is the specific heat capacity of brass, and
ΔT is the change in temperature.
First, let's calculate the heat energy transferred to the statue:
Q = 760 J
Next, we need to know the specific heat capacity of brass. The specific heat capacity of brass is approximately 385 J/kg°C.
c = 385 J/kg°C
The mass of the statue is given as 1 kg.
m = 1 kg
Now, let's calculate the change in temperature (ΔT):
Q = mcΔT
ΔT = Q / (mc)
ΔT = 760 J / (1 kg * 385 J/kg°C)
Simplifying:
ΔT = 760 / 385 °C
Calculating:
ΔT ≈ 1.97 °C
Therefore, the temperature of the brass statue would rise by approximately 1.97 degrees Celsius.
To find the change in temperature of the brass statue, we can use the equation:
Q = mcΔT
Where Q is the heat energy transferred to the statue, m is the mass of the statue, c is the specific heat capacity of brass, and ΔT is the change in temperature.
In this case, we are given the work done against sliding friction, which is equal to the heat energy transferred to the statue. Therefore, we have:
Q = 760 J
The mass of the statue is given as 1 kg.
The specific heat capacity of brass can vary depending on the composition of the brass, but we'll assume it to be 380 J/kg·°C.
Now we can rearrange the equation to solve for ΔT:
ΔT = Q / (mc)
Substituting the given values:
ΔT = 760 J / (1 kg * 380 J/kg·°C)
ΔT = 760 °C / 380
ΔT = 2°C
Therefore, the temperature of the brass statue will rise by 2°C.