Question

consider the following data:

metal

mass (g)

specific heat \\(\left( \frac{\text{j}}{\text{g} \cdot ^\circ \text{c}} \

ight)\\) | temperature (\\(^\circ\text{c}\\)) |

cu	30	0.385	60
pb	12	0.128	30

when these two metals are placed in contact, which of the following will take place?

• heat will flow from cu to pb because cu has a larger specific heat.
• heat will flow from cu to pb because cu has a larger heat capacity.
• no heat will flow in either direction.
• heat will flow from cu to pb because cu has a larger mass.
• heat will flow from cu to pb because cu is at a higher temperature.

Explanation:

Step1: Recall heat transfer principle

Heat flows from a higher - temperature object to a lower - temperature object. The formula for heat capacity \(C = m\times c\), where \(m\) is mass and \(c\) is specific heat. But the direction of heat flow is determined by the temperature difference, not by mass, specific heat, or heat capacity alone.

Step2: Analyze the temperature of the two metals

The temperature of \(Cu\) is \(60^{\circ}C\) and the temperature of \(Pb\) is \(30^{\circ}C\). Since \(60^{\circ}C>30^{\circ}C\), according to the principle of heat transfer (heat flows from a body at higher temperature to a body at lower temperature), heat will flow from \(Cu\) (higher temperature) to \(Pb\) (lower temperature).

Let's also check the other options:

• Option 1: Specific heat is the amount of heat required to raise the temperature of 1 gram of a substance by \(1^{\circ}C\). The direction of heat flow is not determined by specific heat. So this option is wrong.
• Option 2: Calculate heat capacity of \(Cu\): \(C_{Cu}=m_{Cu}\times c_{Cu}=30\ g\times0.385\ \frac{J}{g\cdot^{\circ}C}=11.55\ J/^{\circ}C\). Heat capacity of \(Pb\): \(C_{Pb}=m_{Pb}\times c_{Pb}=12\ g\times0.128\ \frac{J}{g\cdot^{\circ}C} = 1.536\ J/^{\circ}C\). But heat flow direction is based on temperature, not heat capacity. So this option is wrong.
• Option 3: Since there is a temperature difference (\(60^{\circ}C\) vs \(30^{\circ}C\)), heat will flow. So this option is wrong.
• Option 4: Mass does not determine the direction of heat flow. Heat flow is based on temperature difference. So this option is wrong.

Answer:

Heat will flow from Cu to Pb because Cu is at a higher temperature.