# Homework 58


Q10.34

Identify each energy exchange as primarily heat or work and determine the sign $\triangle E$(positive or negative) for the system.

A.) A soccer ball strikes into another soccer ball causing the soccer ball to stop rolling (The first soccer ball is defined as the system).

B.) A military aircraft drops a bomb from the airplane, as the bomb drops, it hits the ground. (The bomb is defined as a system).

C.). Two little girls is on a seesaw (the seesaw and the girls are defined as the system).

Definitions:

Heat : The transfer between two objects due to the temperature difference

Work : A force acting over distance

Energy: The ability of a system to do work or produce heat

Kinetic Energy: when an object gains extra energy due to its motion

Potential Energy: Can be converted to different forms of energy and still be able to do work in the process

Equations

Relationship between Internal Energy $\left ( \triangle E \right )$, Heat (q), and Work (w)

$\triangle E=q+w$

Energy Flow between System and Surroundings

$\triangle Esystem=-\triangle surroundings$

Form of Energy for Heat

Heat-----> Kinetic Energy

Kinetic Energy ----> Potential Energy

Potential Energy---> Kinetic Energy

Strategy

Step 1. Determine whether if each question is performing heat or work

Step 2. Once you figured out if each system is producing heat or work, you can then determine whether your system is positive or negative

Step 3. You're all done

Solutions With Explanations

A.) Work, $-\triangle E$

- So since the first soccer ball collided into the second soccer ball, we can define that it is an example of work because the first soccer ball had to have had some type of force for it to be able to collide into the second soccer ball.

-Now that we have concluded that the soccer ball is producing work, we can also conclude that the delta E is negative because before the soccer ball was kicked, it started off as Kinetic Energy. But once it struck the second soccer ball, it released all of that energy it had formed and created potential energy .

B.) Work, $-\triangle E$

-The reason why this would be considered to be work is because when the bomb was getting ready to be dropped it was able to show some type of action before it hit the ground.

-The reason why the Delta E would be considered negative is because before dropping of the bomb, the bomb was considered as potential energy due to the energy being stored in the object. But once it was dropping, it formed kinetic energy and was able to gain extra energy due to the motion of the bomb dropping from the airplane.

C.)Work,$+\triangle E$

The reason why this would be considered as work is because as the little girls are going up and down on the seesaw, they are able to use a force to motion the seesaw.

The reason why this is considered to be positive is because both of the little girls are losing energy due to each one using force.

Example: Little Girl A ------releases energy to Little girl B so she can be pushed up on the seesaw causing Little Girl A to be on the ground. Then Little Girl B----releases all of her energy that was given to her and is able to transfer that energy back to Little Girl A causing her to be in the air while Little Girl B is back on the ground.

Q11.44

Ideal Gas Law

A balloon is floating on top of an ocean at a volume of 2.04L at a pressure of 730mmHg and a temperature at 20°C . A sea creature then gets hungry and pulls the balloon down to the bottom of the ocean where the temperature decreases to 5°C while the pressure increases to 1510mmHg . Suppose the balloon can freely increase, calculate the volume of the balloon.

Strategy

Step 1. Figure out which formula corresponds with the Ideal Gas Law

Step 2. Write down everything that is given to you in the problem

Step 3. Convert If you need to

Step 4. Solve for what you're looking for

Solution

Step 1. Equation for Ideal Gas Law:

$PV=NRT$

P: Pressure V: Volume N: Moles R: Ideal Gas Constant $0.08206\frac{atm*mol}{L*K}$ T: Temperature

Step 2. What do we know ?

$P_{1}=730mmHg$ $P_{2}=1510mmHg$

$V_1{}=2.04L$ $V_2{}=?$

$N=?$ $R=0.08206\frac{atm*mol}{L*K}$

$T_{1}=20�C$ $T_{2}=5�C$

Step 3. Convert . The first thing we need to do is to convert the Pressure and the Temperature.

$730mmHg*\frac{1atm}{760mmHg}=0.961atm$ $1510mmHg*\frac{1atm}{760mmHg}=1.97atm$

$20�C+273K=293K$ $5�C+273K=278K$

Step 4. The next thing we need to do is find N (Moles) And cancel out units!!!!

$PV=NRT\rightarrow N=\frac{PV}{RT}\rightarro$ ---------> $N=\frac{(0.961atm)(2.04L)}\left ( 0.08206\frac{atm*mol}\left L*K \right \fr \right )(293K)$ $=0.082mol$

Step 5. Now that we have found our moles, we can now plug it into our equation to find the volume (Don't forget to cancel out your units)!!!!

$PV=NRT\rightarrow V=\frac{NRT}{P}$ --------->$N=\frac{\left ( 0.082mol \right )\left ( 0.08206\frac{atm*mol}{L*K}\left ( 278K \right \right )}{1.97atm}$ = $=0.950L$

Answer:$V_{2}$ =0.950L

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