#### Heat: Solutions to Problems

1. a) 20C = (2 + 273) = 275 K
b) -132 0C = (132 + 273)= 141 K

2. a) 100 K =  (100 - 273) 0C = -173 0C
b) 30 K = (30 - 273) = -2430C
c) 500 K = (500 - 273) = -243 0C

3.  Given:

m = 0.700 kg
c = 920 J/KgK
t = 10 min = 600 s
T1 = 100 0C
T2 = 350C

DT = T2 -T1 =  (350C -100 0C)
= -65K

Find: the heat lost
Solution:

Q = m x c x DT
= (0.700 Kg)(920  J/KgK)(-65K)
= 41 860 J
= 42 KJ

4.  Given:
=  500 mL
m = 500 g = 0.500 kg
c = 4220 J/kgK
t = 4 min = 240 s
T2 = 100 0C
T1 = 200C

DT = T2 -T1 =  (100 0C-200C )
= 80K

Find:
1. the heat gained by the water

2. the power of the kettle
Solution:

a) Q = m x c x DT
= (0.500 kg)(4200  J/kgK)(80K)
= 168 000 J
\ E = 168 000 J

b) P = E/t   \ P = 168 000 J / 240 s
= 700 W

5.  Given:

mcoffee = 200 g = 0.200 kg
mmilk = 15 g = 0.015 kg

clost = 4200 J/kgK *coffee
cgained = 3700 J/kgK *milk

T1 = 65 0C *coffee
T1 = 100C  *milk
Find:

Final temperature of mixture (coffee + milk), let final temperature be T

Solution:

a) Qlost = Qgained

[m x c x DT]coffe = [m x c x DT]milk
(0.200 Kg)(4200  J/kgK)(65 0C-T)

=  (0.015 kg)(3700  J/kgK)(T-10 0C)
\ 546 - 8.4T = 5.55T - 55
601 = 13.95T

Solve for T

\ T = 43.10C,
This is the final temperature