Question

1. how much heat (kj) is needed to raise the temperature of 100.0 grams of water from 25.0°c to 50.0°c?

a) 1.05
b) 0.598
c) 10.5
d) 10450
e) none of the above

1. consider the following specific heats of metals.

metal	specific heat (j/g °c)
copper	0.385
gold	0.128
iron	0.449
silver	0.235

if the same amount of heat is added to 50.0 g samples of each of the metals, which are all at the same temperature, which metal will reach the highest temperature?
a) iron
b) silver
c) copper
d) gold
e) aluminum

Explanation:

Question 29

Step 1: Recall the heat formula

The formula for heat \( q \) is \( q = mc\Delta T \), where \( m \) is mass, \( c \) is specific heat capacity, and \( \Delta T \) is the change in temperature. For water, \( c = 4.184 \, \text{J/g}^\circ\text{C} \).

Step 2: Identify values

\( m = 100.0 \, \text{g} \), \( c = 4.184 \, \text{J/g}^\circ\text{C} \), \( \Delta T = 50.0^\circ\text{C} - 25.0^\circ\text{C} = 25.0^\circ\text{C} \).

Step 3: Calculate heat in joules

Substitute into the formula: \( q = 100.0 \, \text{g} \times 4.184 \, \text{J/g}^\circ\text{C} \times 25.0^\circ\text{C} \)
\( q = 100.0 \times 4.184 \times 25.0 = 10460 \, \text{J} \).

Step 4: Convert to kilojoules

Divide by 1000: \( q = \frac{10460 \, \text{J}}{1000} = 10.46 \, \text{kJ} \approx 10.5 \, \text{kJ} \).

The heat formula is \( q = mc\Delta T \). Rearranged for \( \Delta T \): \( \Delta T = \frac{q}{mc} \). When \( q \) (heat) and \( m \) (mass) are constant, \( \Delta T \) is inversely proportional to \( c \) (specific heat). A smaller \( c \) gives a larger \( \Delta T \), so the metal with the smallest specific heat will reach the highest temperature (since final temp = initial temp + \( \Delta T \), and initial temps are equal).

From the table:

• Aluminum: 0.903
• Copper: 0.385
• Gold: 0.128
• Iron: 0.449
• Silver: 0.235

Gold has the smallest specific heat (0.128), so it will have the largest \( \Delta T \) and thus the highest final temperature.

Answer:

C) 10.5

Question 30