Question

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:

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