A 59.3 G Sample Of Quartz, Which Has A Specific Heat Capacity Of 0.730 J ⋅ G − 1 ⋅ ∘ C − 1 0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1} 0.730 J ⋅ G − 1 ⋅ ∘ C − 1 , Is Put Into A Calorimeter That Contains 150.0 G Of Water. The Temperature Of The Water Starts Off At

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Introduction

When a substance is heated or cooled, it undergoes a change in temperature. This change in temperature is directly related to the amount of heat energy transferred to or from the substance. The specific heat capacity of a substance is a measure of its ability to absorb or release heat energy without a change in temperature. In this scenario, we have a sample of quartz with a specific heat capacity of $0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1}$, which is placed in a calorimeter containing 150.0 g of water. The initial temperature of the water is not specified, but we can assume it is at a certain temperature. As the quartz sample is heated, it will transfer heat energy to the water, causing the temperature of the water to rise.

The Calorimeter Experiment

A calorimeter is a device used to measure the heat energy transferred between two substances. In this experiment, the calorimeter contains 150.0 g of water, which is the substance that will absorb the heat energy transferred from the quartz sample. The specific heat capacity of water is $4.184 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1}$. When the quartz sample is heated, it will transfer heat energy to the water, causing the temperature of the water to rise. The amount of heat energy transferred can be calculated using the formula:

${ Q = mc\Delta T }$

where $Q$ is the amount of heat energy transferred, $m$ is the mass of the substance, $c$ is the specific heat capacity of the substance, and $\Delta T$ is the change in temperature.

Calculating the Heat Energy Transferred

To calculate the heat energy transferred, we need to know the initial and final temperatures of the water. Let's assume the initial temperature of the water is $T_i$ and the final temperature is $T_f$. The change in temperature is given by:

${ \Delta T = T_f - T_i }$

We can use the formula for heat energy transfer to calculate the amount of heat energy transferred:

${ Q = mc\Delta T }$

Substituting the values given in the problem, we get:

${ Q = (150.0 \, \text{g})(4.184 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1})(T_f - T_i) }$

The Heat Energy Transferred by the Quartz Sample

The quartz sample has a specific heat capacity of $0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1}$ and a mass of 59.3 g. When the quartz sample is heated, it will transfer heat energy to the water. The amount of heat energy transferred by the quartz sample can be calculated using the formula:

${ Q = mc\Delta T }$

Substituting the values given in the problem, we get:

${ Q = (59.3 \, \text{g})(0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1})(T_f - T_i) }$

Equating the Heat Energy Transferred

The heat energy transferred by the quartz sample is equal to the heat energy absorbed by the water. We can set up an equation based on this equality:

${ (59.3 \, \text{g})(0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1})(T_f - T_i) = (150.0 \, \text{g})(4.184 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1})(T_f - T_i) }$

Solving for the Change in Temperature

We can simplify the equation by canceling out the common terms:

${ (59.3)(0.730) = (150.0)(4.184) }$

Solving for the change in temperature, we get:

${ T_f - T_i = \frac{(59.3)(0.730)}{(150.0)(4.184)} }$

Calculating the Final Temperature

Now that we have the change in temperature, we can calculate the final temperature of the water. Let's assume the initial temperature of the water is $T_i$. The final temperature is given by:

${ T_f = T_i + \Delta T }$

Substituting the value of the change in temperature, we get:

${ T_f = T_i + \frac{(59.3)(0.730)}{(150.0)(4.184)} }$

Conclusion

In this problem, we have a sample of quartz with a specific heat capacity of $0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1}$, which is placed in a calorimeter containing 150.0 g of water. The initial temperature of the water is not specified, but we can assume it is at a certain temperature. As the quartz sample is heated, it will transfer heat energy to the water, causing the temperature of the water to rise. We can calculate the heat energy transferred by the quartz sample and equate it to the heat energy absorbed by the water. By solving for the change in temperature, we can calculate the final temperature of the water.

Final Answer

The final answer is: $\boxed{0.25}$

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Introduction

When a substance is heated or cooled, it undergoes a change in temperature. This change in temperature is directly related to the amount of heat energy transferred to or from the substance. The specific heat capacity of a substance is a measure of its ability to absorb or release heat energy without a change in temperature. In this scenario, we have a sample of quartz with a specific heat capacity of $0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1}$, which is placed in a calorimeter containing 150.0 g of water. The initial temperature of the water is not specified, but we can assume it is at a certain temperature. As the quartz sample is heated, it will transfer heat energy to the water, causing the temperature of the water to rise.

The Calorimeter Experiment

A calorimeter is a device used to measure the heat energy transferred between two substances. In this experiment, the calorimeter contains 150.0 g of water, which is the substance that will absorb the heat energy transferred from the quartz sample. The specific heat capacity of water is $4.184 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1}$. When the quartz sample is heated, it will transfer heat energy to the water, causing the temperature of the water to rise. The amount of heat energy transferred can be calculated using the formula:

${ Q = mc\Delta T }$

where $Q$ is the amount of heat energy transferred, $m$ is the mass of the substance, $c$ is the specific heat capacity of the substance, and $\Delta T$ is the change in temperature.

Calculating the Heat Energy Transferred

To calculate the heat energy transferred, we need to know the initial and final temperatures of the water. Let's assume the initial temperature of the water is $T_i$ and the final temperature is $T_f$. The change in temperature is given by:

${ \Delta T = T_f - T_i }$

We can use the formula for heat energy transfer to calculate the amount of heat energy transferred:

${ Q = mc\Delta T }$

Substituting the values given in the problem, we get:

${ Q = (150.0 \, \text{g})(4.184 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1})(T_f - T_i) }$

The Heat Energy Transferred by the Quartz Sample

The quartz sample has a specific heat capacity of $0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1}$ and a mass of 59.3 g. When the quartz sample is heated, it will transfer heat energy to the water. The amount of heat energy transferred by the quartz sample can be calculated using the formula:

${ Q = mc\Delta T }$

Substituting the values given in the problem, we get:

${ Q = (59.3 \, \text{g})(0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1})(T_f - T_i) }$

Equating the Heat Energy Transferred

The heat energy transferred by the quartz sample is equal to the heat energy absorbed by the water. We can set up an equation based on this equality:

${ (59.3 \, \text{g})(0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1})(T_f - T_i) = (150.0 \, \text{g})(4.184 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1})(T_f - T_i) }$

Solving for the Change in Temperature

We can simplify the equation by canceling out the common terms:

${ (59.3)(0.730) = (150.0)(4.184) }$

Solving for the change in temperature, we get:

${ T_f - T_i = \frac{(59.3)(0.730)}{(150.0)(4.184)} }$

Calculating the Final Temperature

Now that we have the change in temperature, we can calculate the final temperature of the water. Let's assume the initial temperature of the water is $T_i$. The final temperature is given by:

${ T_f = T_i + \Delta T }$

Substituting the value of the change in temperature, we get:

${ T_f = T_i + \frac{(59.3)(0.730)}{(150.0)(4.184)} }$

Conclusion

In this problem, we have a sample of quartz with a specific heat capacity of $0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1}$, which is placed in a calorimeter containing 150.0 g of water. The initial temperature of the water is not specified, but we can assume it is at a certain temperature. As the quartz sample is heated, it will transfer heat energy to the water, causing the temperature of the water to rise. We can calculate the heat energy transferred by the quartz sample and equate it to the heat energy absorbed by the water. By solving for the change in temperature, we can calculate the final temperature of the water.

Q&A

Q: What is the specific heat capacity of quartz?

A: The specific heat capacity of quartz is $0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1}$.

Q: What is the mass of the quartz sample?

A: The mass of the quartz sample is 59.3 g.

Q: What is the mass of the water in the calorimeter?

A: The mass of the water in the calorimeter is 150.0 g.

Q: What is the specific heat capacity of water?

A: The specific heat capacity of water is $4.184 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1}$.

Q: How can we calculate the heat energy transferred by the quartz sample?

A: We can calculate the heat energy transferred by the quartz sample using the formula:

${ Q = mc\Delta T }$

where $Q$ is the amount of heat energy transferred, $m$ is the mass of the substance, $c$ is the specific heat capacity of the substance, and $\Delta T$ is the change in temperature.

Q: How can we equate the heat energy transferred by the quartz sample to the heat energy absorbed by the water?

A: We can equate the heat energy transferred by the quartz sample to the heat energy absorbed by the water by setting up an equation based on the equality:

${ (59.3 \, \text{g})(0.730 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1})(T_f - T_i) = (150.0 \, \text{g})(4.184 \, \text{J} \cdot \text{g}^{-1} \cdot {}^{\circ} \text{C}^{-1})(T_f - T_i) }$

Q: How can we solve for the change in temperature?

A: We can solve for the change in temperature by simplifying the equation and canceling out the common terms:

${ (59.3)(0.730) = (150.0)(4.184) }$

Solving for the change in temperature, we get:

${ T_f - T_i = \frac{(59.3)(0.730)}{(150.0)(4.184)} }$

Q: How can we calculate the final temperature of the water?

A: We can calculate the final temperature of the water by using the formula:

${ T_f = T_i + \Delta T }$

Substituting the value of the change in temperature, we get:

${ T_f = T_i + \frac{(59.3)(0.730)}{(150.0)(4.184)} }$

Final Answer

The final answer is: $\boxed{0.25}$