A lead bullet travelling at 350km/s strikes a target and is brought to rest.What will be the rise in the temperature of the bullet if there is no heat loss to the surrounding

(SHC of Pb is 0.13J/k/kg and melting point of pb=600.5k)

v=350 km/h=350000/3600=97.2 m/s

c=130 J/kg•K
KE -> Q
mv²/2 =cmΔT
ΔT= v²/2c=97.2²/2• 130= 36.3 K

Well, let's tackle this bullet conundrum with a dash of clownish humor!

Ahem. So, the lead bullet is moving at quite the speedy pace, isn't it? 350 kilometers per second? That's faster than a herd of snails on roller skates! Now, when it smacks into the target and comes to a stop, some magical things start happening.

Since there's no heat loss to the surroundings (aww, how considerate!), all of the kinetic energy of the bullet has to transform into thermal energy. Remember, energy can't just disappear, it's not like socks in a washing machine! So, to find out how much the temperature rises, we need to calculate the change in thermal energy.

To do that, we'll use the equation Q = mcΔT, where Q is the thermal energy change, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Now, we know the specific heat capacity of lead (Pb) is 0.13 J/(kg·K), and the melting point of lead is 600.5 K. But we're given one teeny tiny detail: the mass of the bullet? Oh, dear! We're missing that!

Without the mass of the bullet, our clownish calculations become a bit stranded, like a unicycle missing its clown. Alas, I can't provide an answer without all the necessary information. But hey, at least we had a giggle along the way, right?

To calculate the rise in temperature of the lead bullet, we can use the equation:

Q = m * c * ΔT

Where:
Q is the heat energy absorbed by the bullet
m is the mass of the bullet
c is the specific heat capacity of lead
ΔT is the change in temperature of the bullet

First, we need to find the mass of the bullet. Let's assume the mass of the bullet is 1 kg.

m = 1 kg

Next, we need to find the heat energy absorbed by the bullet. The initial kinetic energy (KE) of the bullet is given by:

KE = (1/2) * m * v^2

Where:
m is the mass of the bullet
v is the velocity of the bullet

Since the bullet comes to rest, the initial kinetic energy is converted into heat energy (Q).

Q = KE

Now let's calculate the kinetic energy and the resulting heat energy:

KE = (1/2) * m * v^2
= (1/2) * 1 kg * (350,000 m/s)^2

Next, let's calculate the heat energy absorbed by the bullet:

Q = KE
= (1/2) * 1 kg * (350,000 m/s)^2

Now, let's calculate the change in temperature (ΔT) of the bullet using the specific heat capacity (SHC) of lead:

Q = m * c * ΔT

ΔT = Q / (m * c)
= [ (1/2) * 1 kg * (350,000 m/s)^2 ] / (1 kg * 0.13 J/k/kg)

Finally, let's calculate ΔT:

ΔT = [ (1/2) * (350,000 m/s)^2 ] / (0.13 J/k)
≈ [ (1/2) * (350,000 m/s)^2 ] / 0.13

Note: I have approximated the SHC of lead as 0.13 J/k/kg for simplicity.

To calculate the rise in temperature of the lead bullet, we need to use the principle of conservation of energy. The kinetic energy of the bullet is converted into heat energy when it is brought to rest.

First, let's calculate the kinetic energy of the bullet using the formula:

KE = (1/2) * m * v^2

where:
KE = kinetic energy
m = mass of the bullet
v = velocity of the bullet

We know the mass of the bullet is not given, but we can use the specific heat capacity (SHC) of lead to calculate it. The specific heat capacity (SHC) is the amount of heat energy required to raise the temperature of 1 kg of a substance by 1 degree Celsius.

Given SHC of Pb = 0.13 J/k/kg, we can say that 1 kg of lead requires 0.13 J of energy to increase its temperature by 1 degree Celsius.

Since we don't have the mass, let's assume the mass of the bullet as 1 kg (for simplicity sake). We can always adjust the answer later based on the actual mass of the bullet.

Now, let's calculate the kinetic energy:

KE = (1/2) * m * v^2
= (1/2) * 1 kg * (350,000 m/s)^2

KE = 1.225 * 10^11 J

This is the total kinetic energy of the bullet.

Next, we need to calculate the amount of heat energy required to raise the temperature of the bullet to its melting point.

The heat energy required is given by:

Heat energy = mass * SHC * change in temperature

We know the SHC of lead (0.13 J/k/kg) and the melting point of lead (600.5 K). Let's calculate the change in temperature.

Change in temperature = melting point - initial temperature
= 600.5 K - 298 K (room temperature, assumed)

Change in temperature = 302.5 K

Now, let's calculate the heat energy required:

Heat energy = 1 kg * 0.13 J/k/kg * 302.5 K

Heat energy = 39.325 J

Now, we know that the entire kinetic energy is converted into heat energy, so the rise in temperature is equal to the heat energy required:

Rise in temperature = 39.325 K

Therefore, the rise in temperature of the lead bullet, if there is no heat loss to the surroundings, would be approximately 39.325 degrees Celsius.