Question

Consider two 35-gram ice cubes, each initially at -5°C. One is
dropped into a at container filled with 0.1 kg of liquid nitrogen
(initially the boiling point of nitrogen); the other cube is
dropped into a container filled with 1 kg of (liquid) water,
initially at 5°C. Assume that no heat is lost through either
container (or into the atmosphere).

1.Determine the final (equilibrium) temperature of the
icewater mixture.

2. Determine the phase (ie., liquid or solid) corresponding to
the equilibrium temperature you obtained in part 1.

Answer #1

final temperature = T

initial mass of water, m = 1 kg

initaial temperature of ice = -5C = ti

initial mass of ice . M = 0.035 kg

hence from heat conservation'

energy lost by ice energy gained by water

MLf * Mc(ti) + MC(T - ti) = mC(tw - T)

here, Lf is latent heat of fusion of water, c is heat capacity of
ice, C is heat capacity of water

0.035(333550 + 2108*5 + 4187(T + 5)) = 1*4187(5 - T)

1. T = 1.8827 C

2. Final phase = liquid

Consider two 35-gram ice cubes, each initially at -5°C. One is
dropped into a at container filled with 0.1 kg of liquid nitrogen
(initially the boiling point of nitrogen); the other cube is
dropped into a container filled with 1 kg of (liquid) water,
initially at 5°C. Assume that no heat is lost through either
container (or into the atmosphere)
a) Describe what happens to each ice cube (and why)
b) If (Lv)Nitrogen =48 kcal/kg, (LF)Nitrogen = 6.1 kcal/kg,
and...

Consider two 35-gram ice cubes, each initially at -5°C. One is
dropped into a at container filled with 0.1 kg of liquid nitrogen
(initially the boiling point of nitrogen); the other cube is
dropped into a container filled with 1 kg of (liquid) water,
initially at 5°C. Assume that no heat is lost through either
container (or into the atmosphere)
a) Describe what happens to each ice cube (and why)
b) If (Lv)Nitrogen =48 kcal/kg, (LF)Nitrogen = 6.1 kcal/kg,
and...

(a) Two 64 g ice cubes are dropped into 278 g of water in a
thermally insulated container. If the water is initially at 25°C,
and the ice comes directly from a freezer at −15°C, what is the
final temperature at thermal equilibrium? (in celcius)
(b) What is the final temperature if only one ice cube is used?
(in celcius)

Two 50 gram ice cubes are dropped into 200 grams of water in a
class. 1.) if the water was initially at a temperature of 25
degrees C, and if the ice came directly from a freezer operating at
-15 degrees C, what will be the final temperature of the drink? The
specific heat of ice is about 0.50 cal/(gram degree C) in this
temperature range, and the heat required to melt ice to water is
about 80 cal/gram. 2.)...

(a) You took two 49-gram ice cubes from your -14C kitchen
freezer and placed them in 201 g of water in a thermally insulated
container. If the water is initially at 24C, what is the final
temperature at thermal equilibrium? (b) What is the final
temperature if only one ice cube is used? Hint: Watch out for the
different possibilities!

Three 102.0-g ice cubes initially at 0°C are added to 0.810 kg
of water initially at 18.0°C in an insulated container.
(a) What is the equilibrium temperature of the system?
(b) What is the mass of unmelted ice, if any, when the system is
at equilibrium?

A 39.2 g cube of ice, initially at 0.0 °C, is dropped into 220 g
of water in an 80-g aluminum container. The water is initially at
35 °C and the aluminum container is initially at 25 °C. Remember to
take in to account the melting of the ice. What is the final
equilibrium temperature in °C?

A 35.0-g cube of ice, initially at 0.0°C, is dropped into 180.0
g of water in an 70.0-g aluminum container, both initially at
35.0°C. What is the final equilibrium temperature? (Specific heat
for aluminum is 900 J/kg⋅°C, the specific heat of water is 4 186
J/kg⋅°C, and Lf = 3.33 × 105 J/kg.)
26.4 °C
17.6 °C
8.79 °C
35.1 °C
30.8 ° C

(a) You took two 49-g ice cubes from your −14 C kitchen freezer
and placed them in 201 g of water in a thermally insulated
container. If the water is initially at 24 C, what is the final
temperature at thermal equilibrium? (b) What is the final
temperature if only one ice cube is used? Hint: Watch out for the
different possibilities!

Finding the equilibrium temperature of a mixture: An
isolated thermal system consists of a copper container filled with
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thermalized state of the system (the final temperature, how much
water, and how much ice) provided that initially there is 1.0 kg of
ice at -100 degrees Celsius, 10 kg of water at 1 degrees Celsius,
and the copper container has the mass of 15.0 kg and is...

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