Question

A piece of lead is dropped from a height to 210 M . if 50% of the striking energy is converted into heat calculate the rise in temperature

Answer 1

Given:

Height (h) = 210

Initial velocity (u) = 0 m/s

Acceleration due to gravity (g) =9.8 m/s

Kinetic energy = K.E

Heat energy = Q

Rise in temperature (dt) = ?

Solution:

K.E = 1/2 mv²

= 1/2 m √(u² + 2gh) ⇒(v²=u²+2gh)

= 1/2 m (0² + 2 ₓ 9.8 ₓ 210)

K.E =1/2 m ₓ 4116

Again,

Q = msdt (Here, s is specific heat capacity)

= m ₓ 130 ₓ dt (Value of specific heat capacity of lead is 130 J/kg°C)

Q = 130 ₓ m ₓ dt

According to question,

K.E = Q

1/2 m ₓ 4116 = 130ₓmₓdt

2058/130 = dt

dt = 15.83°C

Therefore, the rise in temperature is 15.83°C.