💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

View Video Answer

Like

Report

A 0.0500-kg ice cube at $-30.0^{\circ} \mathrm{C}$ is placed in 0.400 kg of $35.0^{\circ} \mathrm{C}$ water in a very well-insulated container. What is the final temperature?

$T_{f}=20.6^{\circ} \mathrm{C}$

Physics 101 Mechanics

Chapter 14

Heat and Heat Transfer Methods

Thermal Properties of Matter

Yu J.

April 2, 2022

A heater delivers 1750 W of power to 37.5 kg of air at 15.0oC for 20.0 min. What is the final temperature of the air?

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Lectures

04:16

In mathematics, a proof is…

04:48

In mathematics, algebra is…

05:35

$\bullet$ An insulated bea…

07:10

An insulated beaker with n…

04:18

The temperature of a 0.700…

12:41

A 0.075 -kg ice cube at $0…

05:47

You have 1.50 kg of water …

03:00

A 75.0 -g ice cube at $0^{…

02:40

02:04

Some ice cubes at $0^{\cir…

06:36

32:16

If you pour 0.0100 kg of $…

04:45

A 30.0-g ice cube at its m…

01:52

A 100.-g cube of ice at $0…

01:54

Four ice cubes at exactly …

05:07

What mass of water at $25.…

06:53

In an insulated vessel, $2…

03:18

What will be the final tem…

04:35

In an insulated vessel, 25…

04:21

01:23

A 45 -kg sample of water a…

00:58

If $200 \mathrm{g}$ of wat…

this question is a little more complicated than the other one so far in this chapter. So we're gonna take it slow. Um, in this question, there's some ice cubes that have been put into a glass of water, and we wanna know the final temperature after the ice melts inside the glass of water. So the first concept we want to use is that whatever heat the ice is taking in is just the opposite or negative the heat coming out of the water in the class. So let's block that off and start reading this out. So the total heat it takes to first get the ice to a temperature of zero and then transition into water or melt and then be brought two the final temperature would be we're gonna call this cute I so first that use mass I time specific heat of ice times Delta T to get down to zero. So we know that it starts at a temperature from the equation statement. We know it starts at minus through 30 degrees Celsius, so the final temperature zero minus minus 30 degrees Celsius. Okay, then we have the face transition. That's m I times the latent heat, uh, melting l s plus Now we need to bring it to the final. Temperature is the same equation before burnouts water. So you see of water times the final temperature minus zero. Sense that the temperature of ice. Okay, the other equation weaken right is the heat of war. We know that all the water goes through is the temperature change. So this is just the massive water times the specific Kita Porter That was the final temperature minus. It's original temperature, which is 35 degrees Celsius, as given by the problem statement. So now we can use our quality from the top of the page and equate these sweet of M i C I times 30 degrees Celsius since thes cancel out positive plus and I left plus m i c w t of equals minus Q water. That's, um, W c W We'll break this down since we want to isolate the temperature plus W C W 35 degrees Celsius. His little group are TF terms on one side. So we have from the left hand side, we just have m i c e w t f gonna bring over the m W C W t f from the other side, but everything else over here. So it's M w c W times 35 degrees Celsius from the other side minus. And I see I times 30 degrees Celsius minus again. I left. Okay, so now we're just gonna have t f on the side. Um and we're gonna divide since this is just, let's use red so I can show you what I'm doing here. So these can This can be grouped here into t f times and I plus m w. And you did that seat of you out. So on this side as well, the numerator will be I'm w c w times 35 degrees Celsius minus. We can take out the m I. So it's just see, I comes 30 degrees Celsius waas l f. And then divide by that factor in the other side, which is C w times and I plus Okay, now I'm going to do this math up here so we have a t f. The first, um, piece is MW time. CW's you know, the mass water from the equation is your 0.4 kilograms times the specific eat of water which is 4.1 39 Killer Jules per kilogram degree Celsius times 35 degrees Celsius minus the mass of the ice, which is from the equation from the problem. Others you're queasy. Report five kilograms times sea of ice which is different from sea of water. Needle of that up, which is 2.9 Killa jewels for kilogrammes degrees Celsius times 30 degrees Celsius plus LF which is the latent heat of melting which is 334 kilograms. Killer Jules Rather for killing rooms. Okay, this all gets divided by C W again for 139 Killa jewels for telegrams. Degrees Celsius times the mass of ice plus the mass for Okay, So let's simplify this a little bit. You'll notice that unit's cancel it suffer killer jewels on top here. So we get some numbers. 57.9 Killer Jules minus 19.8 Killer Jules and then on the bottom, cancel out our kilograms again. We get 1.86 Killa Jules per degrees Celsius so you'll see these killer Jules cancel with chemicals in the bottom. We're just left with it with that degree Celsius, which is what we want. So t final do that math should get 20 about 20.5 degrees Celsius

View More Answers From This Book

Find Another Textbook

University of Washington

University of Sheffield

University of Winnipeg

In mathematics, a proof is a sequence of statements given to explain how a c…

In mathematics, algebra is one of the broad parts of mathematics, together w…

$\bullet$ An insulated beaker with negligible mass contains 0.250 $\mathrm{k…

An insulated beaker with negligible mass contains 0.250 $\mathrm{kg}$ of wat…

The temperature of a 0.700 $\mathrm{kg}$ cube of ice is decreased to $-150^{…

A 0.075 -kg ice cube at $0.0^{\circ} \mathrm{C}$ is dropped into a Styrofoam…

You have 1.50 kg of water at 28.0$^\circ$C in an insulated container of negl…

A 75.0 -g ice cube at $0^{\circ} \mathrm{C}$ is placed in 825 $\mathrm{g}$ o…

An insulated beaker with negligible mass contains 0.250 kg of water at 75.0$…

Some ice cubes at $0^{\circ} \mathrm{C}$ with a total mass of 403 $\mathrm{g…

Some ice cubes at $0^{\circ} \mathrm{C}$ with a total mass of $403 \mathrm{g…

If you pour 0.0100 kg of $20.0^{\circ} \mathrm{C}$ water onto a 1.20-kg bloc…

A 30.0-g ice cube at its melting point is dropped into an aluminum calorimet…

A 100.-g cube of ice at $0^{\circ} \mathrm{C}$ is dropped into $1.0 \mathrm{…

Four ice cubes at exactly $0^{\circ} \mathrm{C}$ with a total mass of 53.5 $…

What mass of water at $25.0^{\circ} \mathrm{C}$ added to a Styrofoam cup con…

In an insulated vessel, $250 \mathrm{g}$ of ice at $0^{\circ} \mathrm{C}$ is…

What will be the final temperature of the water in an insulated container as…

In an insulated vessel, 250 g of ice at 0°C is added to 600 g of water at 18…

Four ice cubes at exactly 0 C with a total mass of 53.5 g are combined with…

A 45 -kg sample of water absorbs 345 kJ of heat. If the water was initially …

If $200 \mathrm{g}$ of water at $100^{\circ} \mathrm{C}$ is mixed with $300 …

05:58

(a) How much more intense is a sound that has a level 17.0 dB higher than an…

02:25

Calculate the Reynolds numbers for the flow of water through (a) a nozzle wi…

An airplane passenger has 100 $\mathrm{cm}^{3}$ of air in his stomach just b…

02:39

Unreasonable Results(a) Suppose you want to design a steam engine that h…

03:06

What force must be exerted on the master cylinder of a hydraulic lift to sup…

01:35

With $2.56 \times 10^{6} \mathrm{J}$ of heat transfer into this engine, a gi…

03:01

A sound wave traveling in $20^{\circ} C$ air has a pressure amplitude of 0.5…

00:33

What is the wavelength of the waves you create in a swimming pool if you spl…

03:48

(a) What is the rate of heat conduction through the 3.00 -cm-thick fur of a …

06:09

A simple compass can be made by placing a small bar magnet on a cork floatin…