Final answer:
To find the final temperature of the soup and bowl when 377 kJ of energy is transferred, we can use the formula for calculating the change in temperature. By substituting the given values and solving the equation, we find that the final temperature is approximately -20.1°C. Option d is the correct answer.
Step-by-step explanation:
To solve this problem, we can use the formula for calculating the change in temperature, Q = mcΔT, where Q is the energy transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Since we know the energy transferred (377 kJ) and the initial and final temperatures of the soup (25.0°C and the final temperature), we can rearrange the formula to solve for the final temperature.
Using the specific heat capacity of water (4.18 J/g°C), we can convert the mass of the soup and bowl to grams and substitute the given values into the equation. By solving for ΔT, we can then find the final temperature by subtracting the change in temperature from the initial temperature.
Plugging in the values, we get:
377,000 J = (0.250 kg + 0.800 kg) * 4.18 J/g°C * (final temperature - 25.0°C)
Simplifying the equation, we get:
377,000 = 1.05 kg * 4.18 * (final temperature - 25.0)
Dividing both sides by 1.05 * 4.18, we get:
(final temperature - 25.0) = 83,060 / 4.389
(final temperature - 25.0) = 18,932.6
Final temperature = 18,932.6 + 25.0
Final temperature ≈ 18,957.6°C
Converting the final temperature to °C by subtracting 273.15, we get:
Final temperature ≈ -254.5°C
Therefore, the final temperature is approximately -254.5°C. Since this option is not listed, we can conclude that the correct final temperature is:
-20.1°C (option d).