Chapter 1: Problem 10

You are presented with a block made of some pure metal and told the metal is gold, but you have your doubts. Using a thermometer, how can you determine whether the metal is gold?

Short Answer

Expert verified

To determine if the material is gold using a thermometer, find and compare its specific heat capacity using the equation \(Q=mc\Delta T\). Measure the initial and final temperatures of the block as it's heated, calculate the temperature change, and then find the specific heat capacity of the block. Compare the block's specific heat capacity with gold's known specific heat capacity (0.128 J/g°C). If they closely match, the block might be gold; otherwise, it's likely not gold.

Step by step solution

Measure the initial temperature of the block using a thermometer and record it as \(T_1\). #Step 2: Heat the block#

Apply heat to the block using a known heat source (e.g., placing it in boiling water). It is important to know the amount of heat energy being added to the block so we can calculate the specific heat capacity later. #Step 3: Record the final temperature#

After the block has been heated for a while, measure and record the final temperature as \(T_2\). #Step 4: Determine the temperature change#

Calculate the temperature change, \(\Delta T\), by subtracting the initial temperature from the final temperature: \(\Delta T = T_2 - T_1\) #Step 5: Calculate the heat energy absorbed by the block#

Use the known amount of heat energy applied to the block to determine the heat energy absorbed by the block, represented as Q. #Step 6: Measure the mass of the block#

Using a scale, measure the mass of the block, represented as m. #Step 7: Calculate the specific heat capacity of the block#

Using the equation \(Q = mc\Delta T\), rearrange for c (specific heat capacity) and solve: \(c = \frac{Q}{m\Delta T}\) Calculate c for the block using the heat energy (Q), mass (m), and temperature change (\(\Delta T\)). #Step 8: Compare the calculated specific heat capacity to gold's specific heat capacity#

Compare the calculated specific heat capacity (c) of the block to the known specific heat capacity of gold (approximately 0.128 J/g°C). If they are similar, it is possible that the block is made of gold. If they are significantly different, the block is likely not gold. Keep in mind that experimental errors might result in some disparity, so consider consulting additional testing methods for confirmation.

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You are presented with a block made of some pure metal and told the metal is gold, but you have your doubts. Using a thermometer, how can you determine whether the metal is gold?

Short Answer

Step by step solution

Measure the initial temperature of the block using a thermometer and record it as \(T_1\). #Step 2: Heat the block#

After the block has been heated for a while, measure and record the final temperature as \(T_2\). #Step 4: Determine the temperature change#

Use the known amount of heat energy applied to the block to determine the heat energy absorbed by the block, represented as Q. #Step 6: Measure the mass of the block#

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