the brake linings of the wheels of a car have total mass 4.8kg and specific heat capacity 1200 J kg -1 K-1. calculate the maximum possible temperature rise of the brake linings when the car (of mass 800kg) travelling at 15 ms-1 is brought to rest by applying the brakes.
Well, let's brake it down, shall we?
To calculate the maximum temperature rise of the brake linings, we can use the equation:
ΔQ = mcΔT
Where:
ΔQ is the heat energy transferred
m is the mass of the brake linings (4.8 kg)
c is the specific heat capacity (1200 J kg⁻¹ K⁻¹)
ΔT is the temperature rise
Now, we need to find the heat energy transferred. When the car comes to rest, all of its kinetic energy gets transferred to the brake linings. The kinetic energy is given by:
KE = (1/2)mv²
Where:
m is the mass of the car (800 kg)
v is the velocity of the car (15 m/s)
Plugging in the values, we have:
KE = (1/2)(800 kg)(15 m/s)²
Solving for KE, we get:
KE = 900000 J
Since all of this kinetic energy is transferred to the brake linings, we have:
ΔQ = 900000 J
Now we can rearrange the equation ΔQ = mcΔT to solve for ΔT:
ΔT = ΔQ / (mc)
Plugging in the values, we get:
ΔT = (900000 J) / ((4.8 kg)(1200 J kg⁻¹ K⁻¹))
Simplifying further:
ΔT = 156.25 K
So, the maximum possible temperature rise of the brake linings when the car is brought to rest is approximately 156.25 degrees Celsius. That'll heat things up for sure!
To calculate the maximum possible temperature rise of the brake linings, we need to use the formula:
Q = mcΔT
Where:
Q is the heat energy transferred to the brake linings
m is the mass of the brake linings
c is the specific heat capacity of the brake linings
ΔT is the temperature change.
First, let's calculate the initial kinetic energy (KE) of the car:
KE = (1/2)mv^2
Where:
m is the mass of the car
v is the velocity of the car
KE = (1/2)(800 kg)(15 m/s)^2
KE = 900,000 J
Since the car is brought to rest, all of the initial kinetic energy is transferred to the brake linings in the form of heat. Therefore, this heat energy is equal to the change in internal energy of the brake linings:
Q = ΔU = mcΔT
Rearranging the formula, we get:
ΔT = Q / (mc)
Given:
m = 4.8 kg (mass of the brake linings)
c = 1200 J kg^(-1) K^(-1) (specific heat capacity of the brake linings)
Now we can substitute the values into the formula:
ΔT = 900,000 J / (4.8 kg * 1200 J kg^(-1) K^(-1))
ΔT = 156.25 K
Therefore, the maximum possible temperature rise of the brake linings is 156.25 K.
To calculate the maximum possible temperature rise of the brake linings, we need to use the formula:
Q = mc∆T
where:
Q is the heat transferred (in Joules),
m is the mass of the brake linings (in kilograms),
c is the specific heat capacity of the brake linings (in J/kg·K), and
∆T is the temperature rise (in Kelvin).
To calculate Q, we need to determine the change in kinetic energy (∆KE) of the car when it is brought to rest. The change in KE can be calculated using the formula:
∆KE = 0.5mv²
where:
m is the mass of the car (in kilograms), and
v is the velocity of the car (in meters per second).
In this case, the mass of the car is given as 800 kg and the velocity is given as 15 m/s. So, we can calculate the change in kinetic energy:
∆KE = 0.5 * 800 kg * (15 m/s)²
Next, we can calculate the heat transferred to the brake linings using the equation:
Q = ∆KE
Substituting the values:
Q = (0.5 * 800 kg * (15 m/s)²)
Finally, we can calculate the temperature rise (∆T) using the formula:
∆T = Q / (mc)
Substituting the values, where:
m = 4.8 kg (mass of the brake linings)
c = 1200 J/kg·K (specific heat capacity of the brake linings)
∆T = ((0.5 * 800 kg * (15 m/s)²) / (4.8 kg * 1200 J/kg·K))
Calculating this expression will give you the maximum possible temperature rise of the brake linings.