August 1, 2021

# Solution Set 1

Physics 208-02 – Introductory Physics II
Solution Set 1
Nazareth College
Department of Chemistry & Biochemistry
Robert F Szalapski, PhD – Adjunct Lecturer
www.CallMeDrRob.com
Fall 2011

## § Chapter 13, Problem 5

### § (a)

below zero on the Celsius scale is what Fahrenheit temperature?

### § (b)

below zero on the Fahrenheit scale is what Celsius temperature?

## § Chapter 13, Problem 7

A concrete highway is built of slabs long at . How wide should the expansion cracks be (at ) to prevent buckling if the range of temperatures is to ?

We will need the coefficient of linear expansion for concrete given by

The coefficient is positive, so we should expect that the concrete will contract at lower temperatures and expand at higher temperatures. The maximum expansion will be by an amount

As we see in the figure, if we assume that the slab expands symmetrically, then with an expansion by , it expands by into each gap, but the adjacent slab does the same. Therefore the gap must be .

The gaps between the slabs are often filled with a compressible board that sets the gap properly. This is because the gaps may fill with water, and water has the unusual property that it actually expands when it freezes. Hence, allowing the gaps to fill with ice can lead to buckling and fracturing.

## § Chapter 13, Problem 10

To make a secure fit rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet in diameter is to be placed in a hole in diameter at . To what temperature must the rivet be cooled to fit into the hole?

We will need the coefficient of linear expansion for steel given by

Then

may be rewritten as

Indeed the negative sign indicates cooling.
With

At atmospheric pressure dry ice has a temperature of or colder, so it would be adequate as suggested by the problem statement.

## § Chapter 13, Problem 12

A quartz sphere is in diameter. What will be its change in volume if it is heated from to ?

We will need to know the initial volume of the sphere.

Then

## § Chapter 13, Problem 13

An ordinary glass is filled to the brim with of water at . If the temperature decreased to , how much water could be added to the glass?

Calculate the change in volume for the glass and for the water.

To calculate the available space, subtract the volume of the water from the volume of the glass.

## § Chapter 13, Problem 29

If of a gas initially at STP is placed under a pressure of , the temperature of the gas rises to . What is the volume?

Pressure, volume and temperature are all changing. Only the quantity measured in moles remains the same.

Dividing the first equation by the second,

Using STP to determine the initial temperature and pressure,

## § Chapter 13, Problem 30

In an internal combustion engine air at atmospheric pressure and a temperature of about is compressed in the cylinder by a piston to about of its original volume (compression ratio). Estimate the temperature of the compressed air assuming the pressure reaches .

This is similar to the previous problem, so we begin with

We are also given

which simplifies the equation further.

Substituting the numbers,

## § Chapter 13, Problem 33

A storage tank at STP contains of nitrogen ().

### § (a)

What is the volume of the tank?

Here we must use the full form of the Ideal Gas Law.

First we must find the number of moles of gas noting that the molecular weight is twice the atomic weight of nitrogen.

Hence

The last statement is a good check of our math since we know the molar volume of a mole of ideal gas at STP.

### § (b)

What is the pressure if an additional of nitrogen is added without changing the temperature?

Allowing only and to change,

Dividing the first equation by the second,

We now have

Hence