Chapter 20, Problem 20.1QQ

(a)

To determine

The order of the samples from highest to lowest temperature.

Answer to Problem 20.1QQ

The temperature order is $\text{iron}>\text{glass}>\text{water}$.

Explanation of Solution

Given info: The mass of each sample is $\text{1}\text{.0}\text{kg}$ temperature of each sample is $\text{10}\text{.0°C}$. The energy given to each sample is $\text{100}\text{J}$

The specific heat of iron is $\text{448}\text{J}/\text{kg}\cdot \text{°C}$, the specific heat of water is $4186\text{J}/\text{kg}\cdot \text{°C}$, the specific heat of glass is $837\text{J}/\text{kg}\cdot \text{°C}$

The formula to calculate energy is,

$E=mc\Delta T$ (1)

Here,

$E$ is the energy.

$m$ is the mass of the sample.

$\Delta T$ is the change in the temperature.

$c$ is the specific heat of the sample.

From equation (1), formula to calculate the change in the temperature is

$\begin{array}{l}E=mc\Delta T\\ \Delta T=\frac{E}{mc}\end{array}$ (2)

Form equation (2), the change is temperature is inversely proportional to the specific heat. So larger the specific heat smaller is the change in temperature.

The specific heat of water is highest so the temperature change is the smallest. The specific heat of glass is less than water but greater than water so temperatures change in glass will be more than water but less than iron and the specific heat of iron is least so the temperature change in iron is most.

Conclusion:

Therefore, temperature order is $\text{iron}>\text{glass}>\text{water}$.

(b)

To determine

The rank of the samples from greatest to least amount of energy.

Answer to Problem 20.1QQ

The order from greatest to least energy transferred is $\text{water}>\text{glass}>\text{iron}$.

Explanation of Solution

Given info: The mass of each sample is $\text{1}\text{.0}\text{kg}$ temperature of each sample is raised to $\text{20}\text{.0°C}$. The energy given to each sample is $\text{100}\text{J}$

The specific heat of iron is $\text{448}\text{J}/\text{kg}\cdot \text{°C}$, the specific heat of water is $4186\text{J}/\text{kg}\cdot \text{°C}$ and the specific heat of glass is $837\text{J}/\text{kg}\cdot \text{°C}$

The formula to calculate energy is,

$E=mc\Delta T$ (3)

Here,

$E$ is the energy.

$m$ is the mass of the sample.

$\Delta T$ is the change in the temperature.

$c$ is the specific heat of the sample.

Form equation (3), the energy of the sample is directly proportional to the specific heat of the sample as the mass of each sample and temperature change in the samples are same.

The higher is the specific heat higher the energy will be transferred into the sample for the given temperature increase. So the energy of water will be greatest as it has highest specific heat capacity then the energy of the glass as it has second highest specific heat capacity and then the energy will be least in iron as it has specific heat lowest.

Conclusion:

Therefore, the order from greatest to least energy transferred will be $\text{water}>\text{glass}>\text{iron}$.