Chapter 12, Problem 51A

To determine

The rank according to the amount of thermal energy transferred to methanol from least to greatest.

Answer to Problem 51A

  $Q_D<Q_E<Q_C<Q_A<Q_B$

Explanation of Solution

Given:

The given materials are,

A.50 g of aluminum at $30{\text{}}^o\text{C}$

B.60 g of aluminum at $40{\text{}}^o\text{C}$

C.50 g of glass at $30{\text{}}^o\text{C}$

D.50 g of silver at $30{\text{}}^o\text{C}$

E.50g of zinc at $30{\text{}}^o\text{C}$

Methanol at room temperature.

Formula Used:

The heat transfer can be obtained using:

  $Q=mC\Delta T$

Where, $m$ is mass, $C$ is specific heat capacity and $\Delta T$ is difference in temperature.

Calculation:

For A:

50 g of aluminum at $30{\text{}}^o\text{C}$

As for aluminum specific heat capacity is $C=900\text{J/kg}{-}^o\text{C}$ , so heat transferred is

  $\begin{array}{l}{Q}_A=mC\Delta T\\ =0.05\times 900\times \left({30}^o-25{\text{}}^o\right)\\ =225\text{J}\end{array}$

For B:

60 g of aluminum at $40{\text{}}^o\text{C}$

As for aluminum specific heat capacity is $C=900\text{J/kg}{-}^o\text{C}$ , so heat transferred is

  $\begin{array}{l}{Q}_B=mC\Delta T\\ =0.06\times 900\times \left({40}^o-25{\text{}}^o\right)\\ =810\text{J}\end{array}$

For C:

50 g of glass at $30{\text{}}^o\text{C}$

As for glass specific heat capacity is $C=840\text{J/kg}{-}^o\text{C}$ , so heat transferred is

  $\begin{array}{l}{Q}_C=mC\Delta T\\ =0.05\times 840\times \left({30}^o-25{\text{}}^o\right)\\ =210\text{J}\end{array}$

For D:

50 g of silver at $30{\text{}}^o\text{C}$

As for silver specific heat capacity is $C=230\text{J/kg}{-}^o\text{C}$ , so heat transferred is

  $\begin{array}{l}{Q}_D=mC\Delta T\\ =0.05\times 230\times \left({30}^o-25{\text{}}^o\right)\\ =57.5\text{J}\end{array}$

For E:

50 g of zinc at $30{\text{}}^o\text{C}$

As for zinc specific heat capacity is $C=388\text{J/kg}{-}^o\text{C}$ , so heat transferred is

  $\begin{array}{l}{Q}_E=mC\Delta T\\ =0.05\times 388\times \left({30}^o-25{\text{}}^o\right)\\ =97\text{J}\end{array}$

Conclusion:

So, the thermal energy transferred ranking is $Q_D<Q_E<Q_C<Q_A<Q_B$ .