Mr. Harris assigned his class the task to identify and order unknown liquids by their specific heat. Four liquids are heated at the same temperature setting for ten minutes. The temperature change of each sample is recorded in the table above. Order the unknown liquid samples by specific heat from lowest to highest.

Question

Temperature Change of Liquid Samples
Sample Mass (grams) Start Temperature (°C) Ending Temperature (°C)
1 200 23 69
2 200 20 67
3 200 21 65
4 200 22 70

Answer 1

To determine the specific heat of each liquid sample, we can use the formula:

\[ q = mc\Delta T \]

where:

• \( q \) = heat energy (which is constant for all samples since they were heated in the same way)
• \( m \) = mass of the liquid (given as 200 grams for all samples)
• \( c \) = specific heat of the liquid
• \( \Delta T \) = change in temperature

First, we need to calculate the temperature change (\( \Delta T \)) for each sample:

1. Sample 1:

   • Start Temperature = 23°C
   • End Temperature = 69°C
   • \( \Delta T = 69°C - 23°C = 46°C \)

2. Sample 2:

   • Start Temperature = 20°C
   • End Temperature = 67°C
   • \( \Delta T = 67°C - 20°C = 47°C \)

3. Sample 3:

   • Start Temperature = 21°C
   • End Temperature = 65°C
   • \( \Delta T = 65°C - 21°C = 44°C \)

4. Sample 4:

   • Start Temperature = 22°C
   • End Temperature = 70°C
   • \( \Delta T = 70°C - 22°C = 48°C \)

Now we have the temperature changes for each sample:

• Sample 1: \( \Delta T = 46°C \)
• Sample 2: \( \Delta T = 47°C \)
• Sample 3: \( \Delta T = 44°C \)
• Sample 4: \( \Delta T = 48°C \)

Since \( q \) is the same for all samples and the mass \( m \) is the same, the specific heat \( c \) can be determined by the temperature change. The specific heat is inversely proportional to the temperature change; the larger the temperature change, the lower the specific heat.

Now, we can order the samples by their temperature change from lowest to highest:

1. Sample 3: \( \Delta T = 44°C \) (highest specific heat)
2. Sample 1: \( \Delta T = 46°C \)
3. Sample 2: \( \Delta T = 47°C \)
4. Sample 4: \( \Delta T = 48°C \) (lowest specific heat)

Thus, the order of the unknown liquid samples by specific heat from lowest to highest is:

Sample 4 < Sample 2 < Sample 1 < Sample 3.