To find out how much heat is needed to boil the entire sample of water, you can use the formula:
\[ Q = m \cdot L \]
where:
- \( Q \) is the heat required,
- \( m \) is the mass of the water, and
- \( L \) is the heat of vaporization.
In your case:
- \( m = 200 , \text{g} \)
- \( L = 2260 , \text{J/g} \)
Now, substituting the values into the formula:
\[ Q = 200 , \text{g} \times 2260 , \text{J/g} \]
Calculating this gives:
\[ Q = 452000 , \text{J} \]
So, the amount of heat needed to boil the entire sample of water is \( 452000 , \text{J} \).
The answer is \( 452000 , \text{J} \).