KVPY 2016 SA Question 21

Classical Mechanics Level 3

A $20 \text { g}$ bullet whose specific heat is $5000 \text{ J/kg/}^\circ \text C$ and moving $2000\text{ m/s}$ plunges into a $1.0 \text{ kg}$ block of wax whose specific heat is $3000 \text{ J/kg/}^\circ \text C$ . Both bullet and wax are at $25^\circ \text C$ . Which of the options is the temperature of the wax close to?

Assumptions:

The bullet comes to rest in the wax.
All the kinetic energy of the bullet goes into heating the wax.

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31.5^\circ \text C

42.1^\circ \text C

28.1^\circ \text C

37.9^\circ \text C

1 solution

Chew-Seong Cheong
Feb 28, 2017

Assuming all the kinetic energy is converted into heat, we have:

$\begin{aligned} \frac 12 m_bv^2 & = m_bC_g(\theta-\theta_i) + m_wC_w(\theta-\theta_i) \\ \frac {0.02\times 2000^2}2 & = 0.02 \times 5000 (\theta - 25) + 1.0 \times 3000 (\theta - 25) \\ 40000 & = 3100(\theta - 25) \\ \implies \theta & = \frac {40000}{3100} + 25 \\ & \approx \boxed{37.9^\circ \text C} \end{aligned}$

Notations:

$m_b$ and $m_w$ , the masses of the bullet and wax respectively
$C_b$ and $C_w$ , the specific heats of the bullet and wax respectively
$v$ , velocity of the bullet
$\theta$ , the final temperature of the bullet and wax when heat transfer is complete
$\theta_i$ , the initial temperature of the bullet and wax

KVPY 2016 SA Question 21

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