Gloves are often worn to protect the hands from being burned when they come in contact with very hot or very cold objects. Gloves are often made of cotton or wool, but many of the newer heat-resistant gloves are made of silicon rubber. The specific heats of these materials are listed below: $$ \begin{array}{|l|c|} \hline \text { Material } & \text { Specific heat }\left(\mathbf{J} / \mathrm{g}^{\circ} \mathbf{C}\right) \\ \hline \text { wool felt } & 1.38 \\ \hline \text { cotton } & 1.33 \\ \hline \text { paper } & 1.33 \\ \hline \text { rubber } & 3.65 \\ \hline \text { silicon rubber } & 1.46 \\ \hline \end{array} $$ (a) If a glove with a mass of \(99.3\) grams composed of cotton increases in temperature by \(15.3^{\circ} \mathrm{F}\), how much energy was absorbed by the glove? (b) A glove with a mass of \(86.2\) grams increases in temperature by \(25.9^{\circ} \mathrm{F}\) when it absorbs \(1.71 \mathrm{~kJ}\) of energy. Calculate the specific heat of the glove and predict its composition. (c) If a glove with a mass of \(50.0\) grams needs to absorb \(1.65 \mathrm{~kJ}\) of energy, how much will the temperature of the glove increase for each of the materials listed above? (d) Which is the best material for a heat-resistant glove? (e) If you were designing a heat-resistant glove, what kind of specific heat would you look for?

Step by step solution

01

Understand Specific Heat Capacity

Specific heat capacity (c) is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C. The formula to calculate the energy absorbed (q) is given by: \[ q = m \times c \times \triangle T \] where m is mass, c is specific heat capacity, and \triangle T is the temperature change.

02

Step 2a: Convert Temperature Change for Question (a)

Since the temperature change is given in °F, convert it to °C using the formula: \[ \triangle T (\text{°C}) = \frac{\triangle T (\text{°F}) - 32}{1.8} \] For \triangle T = 15.3\text{°F}, we get: \[ \triangle T (\text{°C}) = \frac{15.3 - 32}{1.8} = 8.5\text{°C} \]

03

Step 3a: Calculate Energy Absorbed for Cotton Glove

Given: \[ m = 99.3 \text{ g}, \triangle T = 8.5\text{°C}, \text{ and } c = 1.33 \frac{\text{J}}{\text{g}\text{°C}} \] Substitute these values into the formula: \[ q = 99.3 \times 1.33 \times 8.5 = 1125.44 \text{ J} \]

04

Step 4a: Convert Joules to Kilojoules for Part (a)

Convert the energy from Joules to Kilojoules: \[ 1125.44 \text{ J} = 1.12544 \text{ kJ} \] The energy absorbed by the glove is approximately 1.13 kJ.

05

Step 2b: Convert Temperature Change for Question (b)

For \triangle T = 25.9\text{°F}, we get: \[ \triangle T (\text{°C}) = \frac{25.9 - 32}{1.8} = 14.39\text{°C} \]

06

Step 3b: Calculate Specific Heat for Part (b)

Use the formula \[ c = \frac{q}{m \times \triangle T} \] Given: \[ q = 1710 \text{ J} (since 1.71 \text{ kJ} = 1710 \text{ J}), m = 86.2 \text{ g}, \triangle T = 14.39\text{°C} \] Substitute these values: \[ c = \frac{1710}{86.2 \times 14.39} = 1.38 \frac{\text{J}}{\text{g}\text{°C}} \] The specific heat is 1.38, which matches wool felt.

07

Step 2c: Calculate Temperature Increase for Part (c)

Use the formula: \[ \triangle T = \frac{q}{m \times c} \] Given: \[ q = 1650 \text{ J} (since 1.65 \text{ kJ} = 1650 \text{ J}), m = 50.0 \text{ g} \] Calculate \triangle T for each material: \[ \text{Wool}: \triangle T = \frac{1650}{50 \times 1.38} = 23.91 \text{°C} \] \[ \text{Cotton}: \triangle T = \frac{1650}{50 \times 1.33} = 24.81 \text{°C} \] \[ \text{Paper}: \triangle T = \frac{1650}{50 \times 1.33} = 24.81 \text{°C} \] \[ \text{Rubber}: \triangle T = \frac{1650}{50 \times 3.65} = 9.04 \text{°C} \] \[ \text{Silicon Rubber}: \triangle T = \frac{1650}{50 \times 1.46} = 22.60 \text{°C} \]

08

Step 1d: Identify the Best Heat-Resistant Material

The best heat-resistant material would have the highest specific heat capacity to absorb more energy without a significant increase in temperature. From the given data, rubber has the highest specific heat capacity of 3.65 and thus is the best choice.

09

Step 1e: Specific Heat Capacity for Designing Heat-Resistant Gloves

For designing heat-resistant gloves, look for materials with the highest specific heat capacity as they will absorb more energy without heating up too quickly. Rubber would be a good choice due to its high specific heat capacity.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Heat Transfer

Heat transfer is the process of thermal energy moving from a hotter object to a cooler one. When you wear gloves to handle hot or cold objects, you are controlling the flow of heat to protect your hands. There are three main methods of heat transfer: conduction, convection, and radiation. In the context of gloves, conduction is the primary mode of heat transfer. This is because heat moves directly from the hot (or cold) object to your glove and then to your skin. When you use materials with different specific heat capacities, they affect how much heat is transferred and at what rate. Remember, better heat-resistant gloves reduce the rate at which heat is conducted to your hands, giving you better protection.

Temperature Change

Temperature change \(\Delta T\) refers to the difference in temperature that occurs as a result of heat transfer. It is calculated using the formula \(\Delta T = \frac{\Delta T (\text{°F}) - 32}{1.8}\) when converting from Fahrenheit to Celsius. For example, in part (a) of the exercise, if the temperature of the cotton glove changes by 15.3°F, converting this to Celsius gives you approximately 8.5°C. This change in temperature depends on how much energy is absorbed by the material and its specific heat capacity. A higher specific heat capacity means a smaller temperature change for a given amount of absorbed heat.

Material Properties

Different materials have unique properties such as specific heat capacity, which affects how they absorb and store heat. Specific heat capacity (c) is the amount of heat needed to raise the temperature of 1 gram of a material by 1°C. Materials like rubber have high specific heat capacities (3.65 J/g°C), making them effective at absorbing more heat without a significant rise in temperature. In contrast, materials like cotton and wool have lower specific heat capacities (1.33 J/g°C and 1.38 J/g°C, respectively). This means they heat up more quickly and can become less effective at protecting against heat over prolonged periods. When designing heat-resistant gloves, choosing materials with high specific heat capacities, like rubber, can be key.

Energy Absorption

Energy absorption is the process by which a material takes in energy from its surroundings in the form of heat. The amount of energy absorbed (q) can be calculated using the formula \( q = m \times c \times \Delta T \) where m is mass, c is specific heat capacity, and \(\Delta T\) is temperature change. From the exercise, if a glove made of cotton (99.3 grams) experiences an 8.5°C temperature change, you can find the energy it absorbed by plugging these values into the formula, giving you approximately 1125.44 Joules. This knowledge helps in understanding why different materials behave differently when exposed to heat and underlines the importance of selecting the right material for heat resistance based on how much energy it can absorb before reaching high temperatures.