The element radon is at the opposite end of the range with the lowest specific heat of all naturally occurring elements. At 25°C, radon’s specific heat is 94 J/kg • K. If the temperature of a 0.34 kg sample of radon is to be raised by 25 K, how much energy will have to be added to the radon?

Answer 1

To calculate the amount of energy required to raise the temperature of a substance, we can use the formula:

\[ Q = m \cdot c \cdot \Delta T \]

where:

• \( Q \) is the energy (in joules),
• \( m \) is the mass of the substance (in kg),
• \( c \) is the specific heat capacity (in J/kg·K),
• \( \Delta T \) is the change in temperature (in K).

In this case:

• \( m = 0.34 , \text{kg} \)
• \( c = 94 , \text{J/kg·K} \)
• \( \Delta T = 25 , \text{K} \)

Now, plug in the values:

\[ Q = 0.34 , \text{kg} \cdot 94 , \text{J/kg·K} \cdot 25 , \text{K} \]

Calculating that step-by-step:

1. Calculate \( m \cdot c \): \[ 0.34 , \text{kg} \cdot 94 , \text{J/kg·K} = 31.96 , \text{J/K} \]

2. Now multiply by \( \Delta T \): \[ Q = 31.96 , \text{J/K} \cdot 25 , \text{K} = 799 , \text{J} \]

Thus, the energy required to raise the temperature of the 0.34 kg sample of radon by 25 K is:

\[ \boxed{799 , \text{J}} \]