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Part A

Which of the following substances (with specific heat capacity provided) would show the smallest temperature change upon gaining 200.0 J of heat?

A. 50.0 g water, [tex]C_{\text{water}} = 4.18 \, \text{J/g} \cdot {}^{\circ} \text{C}[/tex]
B. 50.0 g Fe, [tex]C_{\text{Fe}} = 0.449 \, \text{J/g} \cdot {}^{\circ} \text{C}[/tex]
C. 50.0 g granite, [tex]C_{\text{granite}} = 0.79 \, \text{J/g} \cdot {}^{\circ} \text{C}[/tex]
D. 50.0 g Ag, [tex]C_{\text{Ag}} = 0.235 \, \text{J/g} \cdot {}^{\circ} \text{C}[/tex]
E. 25.0 g Pb, [tex]C_{\text{Pb}} = 0.128 \, \text{J/g} \cdot {}^{\circ} \text{C}[/tex]

Sagot :

GinnyAnswer
To determine which substance shows the smallest temperature change upon gaining 200.0 J of heat, we need to calculate the temperature change ([tex]\(\Delta T\)[/tex]) for each substance using the formula:

[tex]\[ \Delta T = \frac{Q}{m \cdot C} \][/tex]

where:
- [tex]\(Q\)[/tex] is the heat added (200.0 J)
- [tex]\(m\)[/tex] is the mass of the substance in grams
- [tex]\(C\)[/tex] is the specific heat capacity in [tex]\(J/(g \cdot °C)\)[/tex]

Let's analyze the given data to find [tex]\(\Delta T\)[/tex] for each substance:

1. Water:
- Mass: [tex]\(50.0 \, g\)[/tex]
- Specific heat capacity ([tex]\(C_{\text{water}}\)[/tex]): [tex]\(4.18 \, J/(g \cdot °C)\)[/tex]
- [tex]\(\Delta T_{\text{water}} = \frac{200.0}{50.0 \cdot 4.18} \approx 0.957°C\)[/tex]

2. Iron (Fe):
- Mass: [tex]\(50.0 \, g\)[/tex]
- Specific heat capacity ([tex]\(C_{\text{Fe}}\)[/tex]): [tex]\(0.449 \, J/(g \cdot °C)\)[/tex]
- [tex]\(\Delta T_{\text{Fe}} = \frac{200.0}{50.0 \cdot 0.449} \approx 8.909°C\)[/tex]

3. Granite:
- Mass: [tex]\(50.0 \, g\)[/tex]
- Specific heat capacity ([tex]\(C_{\text{granite}}\)[/tex]): [tex]\(0.79 \, J/(g \cdot °C)\)[/tex]
- [tex]\(\Delta T_{\text{granite}} = \frac{200.0}{50.0 \cdot 0.79} \approx 5.063°C\)[/tex]

4. Silver (Ag):
- Mass: [tex]\(50.0 \, g\)[/tex]
- Specific heat capacity ([tex]\(C_{\text{Ag}}\)[/tex]): [tex]\(0.235 \, J/(g \cdot °C)\)[/tex]
- [tex]\(\Delta T_{\text{Ag}} = \frac{200.0}{50.0 \cdot 0.235} \approx 17.021°C\)[/tex]

5. Lead (Pb):
- Mass: [tex]\(25.0 \, g\)[/tex]
- Specific heat capacity ([tex]\(C_{\text{Pb}}\)[/tex]): [tex]\(0.128 \, J/(g \cdot °C)\)[/tex]
- [tex]\(\Delta T_{\text{Pb}} = \frac{200.0}{25.0 \cdot 0.128} \approx 62.5°C\)[/tex]

After calculating these temperature changes, we find:

[tex]\[ \Delta T_{\text{water}} \approx 0.957°C \][/tex]
[tex]\[ \Delta T_{\text{Fe}} \approx 8.909°C \][/tex]
[tex]\[ \Delta T_{\text{granite}} \approx 5.063°C \][/tex]
[tex]\[ \Delta T_{\text{Ag}} \approx 17.021°C \][/tex]
[tex]\[ \Delta T_{\text{Pb}} \approx 62.5°C \][/tex]

Comparing all these values, we can see that the smallest temperature change occurs in water, with [tex]\(\Delta T_{\text{water}} \approx 0.957°C\)[/tex].

Therefore, the substance that shows the smallest temperature change upon gaining 200.0 J of heat is 50.0 g of water.
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