Energy to raise temperature of water

[Dazed]

Just looking for someone to check my work on this question before I submit it to the teacher. Any help is appreciated. :)

3. A 0.500 kg pot of hot water for tea has cooled to 40.0 OC. How much freshly boiled water must be added (at 100 OC) to raise the temperature of the tea water to a respectable 65.0 OC?

Let n represent the unknown mass of water to be added.

Starting water + Added water = total water

40c x 0.5 kg + 100c x n = 65 (0.5kg + n)

20 kg + 100 n = (32.5kg + 65n)

52.5 kg = 165 n

1 kg = 3.1n

n = 1/3.1

n = 0.32 kg

To raise the temperature of the tea to 65 degrees, 0.32kg of 100c water must be added.


~Dazed

 

[marcusl]

No, you messed up the third step. Subtract 65n from both sides, and 20 kg, to get
35n = 12.5kg
You can finish it from there.

A small additional note: your units aren't complete, when you multiply temperature times mass, the units are c-kg. Won't matter in the end, but keeping accurate track is a good habit.

 

[Dazed]

Thank you for your reply. :)

I think I've correctly fixed this as per your suggestions, I used the units c/kg instead of c-kg, I assumed that was a typo. If c-kg is correct please tell me and I'll change it. Also please tell me if the new answer is correct or of I messed up somewhere again. :)

3. A 0.500 kg pot of hot water for tea has cooled to 40.0 OC. How much freshly boiled water must be added (at 100 OC) to raise the temperature of the tea water to a respectable 65.0 OC?

Let n represent the unknown mass of water to be added.

Starting water + Added water = Total water

(40c x 0.5 kg) + (100c * n) = 65c(0.5kg + n)

20c/kg + 100n = (32.5c/kg + 65n)

Subtract 65n from both sides
20c/kg + (100n - 65n) = 32.5c/kg + (65n – 65n)

20c/kg + 35n = 32.5c/kg

Subtract 20kg from both sides
(20kg – 20kg) + 35n = (32.5kg – 20kg)

35n = 12.5kg

n = 12.5kg / 35

n = 0.357kg

To raise the temperature of the tea to 65 degrees, 0.357kg of 100c water must be added.

 

[marcusl]

Correct answer. You're units are still a little confused. If you multiply 40c x 0.5 kg, you get 20 c kg (whatever that is!). Then when you get down to
35c * n = 12.5 c kg
and solve, you get
n =12.5 c kg / 35 c
and the answer has units of kg as you knew it must.

 

[SeamusMcGowan]

NO. If you added 0.357kg of water to the pot it would overflow. You would have to add both parts of the water to a 0.900 kg pot and then return 0.500 kg to the original pot.