August 1, 2021

# Exam 1

Physics 208 – Introductory Physics II
Nazareth College
Department of Chemistry & Biochemistry
Robert F Szalapski, PhD – Adjunct Lecturer
www.CallMeDrRob.com
Spring 2012

Exam 1
Heat, Work, Ideal Gases and Phase Changes

## § Potentially Useful Data

Constants:

Conversion Factors:

 Substance c Ammonia (NH) 4,600 Water (l) 4,186 Ice 2,090 Ethanol 2,300 Steam 2,010 Beryllium (Be) 1,820 Air 1,004 Aluminum (Al) 900 Glass 837 Silicon (Si) 703 Iron (steel) 448 Copper (Cu) 387 Silver (Ag) 234 Gold (Au) 129 Lead (Pb) 128

Substance Water (HO) Fusion: Vaporization:

## § Problem 1

On a cold Rochester morning when it is only outside you fill your automobile tank until it holds a total of of gasoline. The temperature then climbs to . How large must your gasoline tank be at so that it does not overflow? (10 points)

First we must convert the temperature difference to Celsius.

Then

Note that most numbers were only specified to a single significant digit, so this is just an estimate. Nevertheless, it is clear that you do not want to fill your gasoline tank to the top of the fill pipe!

## § Problem 2

A canister is open to the air at the room temperature of , and then the cover is closed. Assume that air is approximately an ideal gas.

### § (a)

How many moles of air are inside the canister? (10 points)

The easiest approach is to realize that we are at STP, and we know the molar volume for one mole. We could set up a simple proportion.

The other approach is to use the Ideal Gas Law:

### § (b)

If the canister is heated to but the canister does not expand, then what is the new pressure inside the canister? (10 points)

### § (c)

Maintaining the temperature of , stomp on the canister until its volume is reduced by one-third. What is the pressure inside now? (10 points)

Reduced by one-third means

### § (d)

Allow the canister to return to the original room temperature. What is the final pressure? (10 points)

There are two good approaches. We can use the results from (c):

The thing about the Ideal Gas Law is that it describes the current state of the gas in terms of the state variables. It is not important what path led to that state. Hence we could realize that only the pressure and volume are now different from the initial state while and are back to their original values. Hence

## § Problem 3

100 g of is initially at a temperature of . It is placed in a calorimeter where it is heated to . The temperature of the is recorded as a function of time.

### § (a)

Make a plot of temperature versus time for the experiment. Label the axes, all temperatures of significance, and the phases involved in each segment of the graph. (10 points)

### § (b)

How much heat was required to heat the ? (Be sure to include heating and phase changes.) (20 points)

There are five steps, warming the ice, melting the ice to water, warming the water, boiling the water and heating the steam.

### § (c)

Suppose the heat required all came from the 2 kg beryllium calorimeter which was initially at a temperature but is in thermal equilibrium with the at the end of the experiment. Calculate . (10 points)

## § Problem 4

A student in Physics 208, wishing to test the equivalence of heat and energy, waits for a day when the temperature outside is exactly . An official men’s collegiate shot-put shot, mass , in thermal equilibrium with its surroundings, is then dropped a distance of into a pile of crushed ice. Estimate the mass of ice that is melted as a result of stopping the shot. (10 points)

Gravitational potential energy will be converted to an equal amount of kinetic energy which in turn will be converted to an equal amount of heat which melts ice. We can leave out the middle step and equate gravitational potentially energy directly with heat.