Question

At which temperature does water have particles with a greater average kinetic energy than water with a temperature of 30°C?

77°F
95°F
280K
300K

Answer 1

To determine which temperature corresponds to water with greater average kinetic energy than water at 30°C, we first need to convert 30°C into Kelvin and Fahrenheit.

1. **Converting 30°C to Kelvin:**
\[
K = C + 273.15
\]
\[
K = 30 + 273.15 = 303.15 \, K
\]

2. **Converting the given temperatures to Celsius or Kelvin:**

- **77°F to Celsius:**
\[
C = \frac{(F - 32) \times 5}{9}
\]
\[
C = \frac{(77 - 32) \times 5}{9} \approx 25°C
\]

- **95°F to Celsius:**
\[
C = \frac{(95 - 32) \times 5}{9} \approx 35°C
\]

- **280K to Celsius:**
\[
C = K - 273.15
\]
\[
C = 280 - 273.15 \approx 6.85°C
\]

- **300K to Celsius:**
\[
C = 300 - 273.15 \approx 26.85°C
\]

3. **Summary of temperatures converted:**
- 30°C = 303.15 K
- 77°F ≈ 25°C (≈ 298 K)
- 95°F ≈ 35°C (≈ 308 K)
- 280 K ≈ 6.85°C
- 300 K ≈ 26.85°C

4. **Comparison:**
- To have greater average kinetic energy, the temperatures must be greater than 30°C (or 303.15 K).
- Among the options:
- 77°F (≈ 25°C) < 30°C
- 95°F (≈ 35°C) > 30°C
- 280 K (≈ 6.85°C) < 30°C
- 300 K (≈ 26.85°C) < 30°C

Therefore, the temperature at which water has particles with a greater average kinetic energy than at 30°C is **95°F**.