Chapter 21, Problem 21A

The four plastic-foam soup bowls contain the same amount of water at $20°C$. You also have a batch of 100-g copper cylinders that have initial temperatures as shown. The cylinders are submerged in the bowls.

Rank the bowls according to the maximum temperature of the water after the cylinders are added.

To determine

To Rank: The bowls as per maximum temperature of water after the cylinders added.

Explanation of Solution

Introduction:

Thermal equilibrium refers to the attainment of same temperature by the two bodies when the thermal energy transfers from one body to another when placed in contact with each other.

The equilibrium temperature depends on the amount of thermal energy transferred which depends on the mass $\left(m\right)$ , difference in temperature $\left(T\right)$ and specific heat $\left(c\right)$ . The mass of cylinders (number) and their temperature is different in each case, so the final temperature of water would be different.

  $T_f=\frac{m_1{c}_1{T}_1+m_2{c}_2{T}_2}{m_1{c}_1+m_2{c}_2}$

Specific heat of plastic foam is $1.3\text{J/g°C}$ .

Specific heat of water is $4.184\text{J/g°C}$

The temperature is high for case B and C but the mass of cylinders in case C is greatest. Thus, the maximum temperature of water would be in case C, then B followed by A and least in case D.

Conclusion:

The rank would be: $C>B>A>D$