Question

If the same amount of heat is added to 25.0 g of each of the metals, which are all at the same initial temperature, which metal will have the highest temperature?
Specific Heats of Metals:
Metal Specific Heat
Copper 0.385 J/(g°C)
Magnesium 1.02 J/(g°C)
Tungsten 0.134 J/(g°C)
Silver 0.237 J/(g°C)
Bismuth 0.123 J/(g°C)

Answer 1

Answer:

The bismuth sample.

Explanation:

The specific heat $c$ of a substance (might not be a metal) is the amount of heat required for heating a unit mass of this substance by unit temperature (e.g., $\rm 1\; ^{\circ}C$.) The formula for specific heat is:

$\displaystyle c = \frac{Q}{m \cdot \Delta T}$,

where

• $Q$ is the amount of heat supplied.
• $m$ is the mass of the sample.
• $\Delta T$ is the increase in temperature.

In this question, the value of $Q$ (amount of heat supplied to the metal) and $m$ (mass of the metal sample) are the same for all four metals. To find $\Delta T$ (change in temperature,) rearrange the equation:

$\displaystyle c \cdot \Delta T = \frac{Q}{m}$,

$\displaystyle \Delta T = \frac{Q}{c \cdot m}$.

In other words, the change in temperature of the sample, $\Delta T$ can be expressed as a fraction. Additionally, the specific heat of sample, $c$, is in the denominator of that fraction. Hence, the value of the fraction would be the largest for sample with the smallest specific heat.

Make sure that all the specific heat values are in the same unit. Find the one with the smallest specific heat: bismuth ($\rm 0.123 \; J \cdot g\cdot \,^{\circ}C^{-1}$.) That sample would have the greatest increase in temperature. Since all six samples started at the same temperature, the bismuth sample would also have the highest final temperature.