The same heat transfer into identical masses of different substances produces different temperat

The same heat transfer into identical masses of different...

Key Concepts

Temperature Change Calculation

This involves using the formula ?T = Q/(mc), where ?T is the change in temperature, Q is the heat energy transferred, m is the mass of the substance, and c is its specific heat capacity. This calculation determines how much the temperature of a substance will rise when a certain amount of heat is added.

Units Conversion

Units conversion is important in thermodynamic calculations, especially when dealing with energy units such as kilocalories and joules. Consistent unit usage ensures that calculations of temperature change are accurate and meaningful.

Heat Transfer

Heat transfer is the process by which thermal energy is exchanged between physical systems due to a temperature difference. It plays a crucial role in understanding how energy is delivered to a substance, which in turn affects its temperature change.

Energy Conservation in Thermal Processes

This concept is governed by the principle that energy cannot be created or destroyed, only transferred or transformed. In thermodynamics, energy conservation is used to relate the amount of heat added to a system (using the equation Q = mc?T) to the resultant change in temperature.

Specific Heat Capacity

This concept refers to the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a key factor that explains why different materials, even with the same mass and starting temperature, experience different temperature changes when exposed to the same amount of heat.

Transcript

00:01 Okay, for this question, we have one kilocalory of heat being transferred into one kilogram of mass for four different types of matter.

00:11 And we have an original temperature, t, of 20 degrees celsius, and we are looking for the final temperature of each of these.

00:23 So for this problem, we want to use the classic heat equation, which is q, the heat, equals m.

00:33 The mass times the specific heat of the material c times delta t so delta t is the same as final temperature minus initial temperature so we can rewrite this equation to say q equals mc times tf minus t o can divide both sides by mc so this gives us tf minus t o so the equation we're going to be working with to solve for tf is, i can't draw it on here, is the original temperature plus q over mc.

01:32 So let's just highlight this.

01:33 We can remember it and separate it from where we're going to solve for these.

01:42 Okay.

01:43 So part a of the question is asking what is the final temperature if the matter involved is water.

01:52 So the specific heat for water, you have to look this up.

01:56 And this is one calorie per gram times degrees celsius.

02:05 So if we plug this into our equation, we have t final equals t not, which is 20 degrees celsius, plus q in all of these is one kilocalories.

02:20 So that's 1 ,000 calories divided by m times c so m is the same for all of these it's one kilogram or 1 ,000 grams we're going to work in kilograms and calories and grams rather because our specific heats are given in calories and grams that's why i'm converting from kilograms and kilocalis so q over mc so we need that specific heat here which is one calorie over grams times degrees celsius.

02:57 So we have a calorie over a calorie and a gram over a gram.

03:01 Those cancel out.

03:02 We also have 1 ,000 over 1 ,000.

03:05 So that's just 1.

03:06 So this is 20 degrees celsius plus 1 degree celsius because the degree celsius comes up top.

03:20 So this gives us our answer for water of 21 degrees celsius.

03:25 Let's circle that.

03:31 So for b, same thing, but our specific heat is 0 .2 calories per gram degrees celsius...