1) I had take-out Vietnamese soup for lunch on Saturday. To make sure the noodle

Question

1) I had take-out Vietnamese soup for lunch on Saturday. To make sure the noodles did not get soggy, they packaged them separately, and then I mixed them to together to make my noodle soup. I had 1 L = 1 kg of broth at T = 80 C, and 0.3 kg of noodles at T = 40 C. The constant pressure heat capacity of the soup and noodles are 4.2 kJ/kg K and 3.0 kJ/kg K, respectively. Assuming no loss of energy to the surroundings and that the soup is at uniform temperature, calculate the final temperature of my noodle soup.

Explanation / Answer

Heat lost by the broth will be equal to the heat gained by the noodles.

Q = mass x specific heat x change in temperature

So let the final temperature be T

So here :

1 x 4.2 x (80 - T) = 0.3 x 3.0 x (T - 40)

336 - 4.2T = 0.9T - 36

336 + 36 = 0.9T + 4.2T

372 = 5.1T

T = 72.94

so the final temperature of the noodle soup will be 72.94 C

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