# Homework Set 10

## Problem 17.8

To solve this problem you need to consider linear thermal expansion. You can use the $l$ given at $20^{o}C$ even though the question asks for $\Delta l$ at $15^{o}C$ ($\Delta l << l$). You will need the linear coefficient of thermal expansion of concrete which can be found here, or in your textbook.

## Problem 17.16

In this problem you need to calculate the volume expansion of the radiator, engine and coolant. The difference between the volume of the coolant and the sum of the volumes of the two containers will be the volume that overflows. You will need the volume coefficients of thermal expansion which you can find either here, or in your textbook.

## Problem 17.42

This problem requires the use of the ideal gas law. Watch out for the correct units of temperature!

## Problem 17.50

Another ideal gas law problem. The temperature is different at the bottom and surface of the lake, but you should also pay attention to the pressure as a function of depth.

## Average Spacing of Gas Molecules

Use $PV=nkT$ with $n=1$. Don't forget to convert the pressure and temperature to the right units!

## Problem 17.65

Another ideal gas law problem. Is the pressure in the ideal gas law absolute or gauge pressure

## Problem 19.13

To solve this problem we need to consider the specific heat of water and glass. We then need to write an equation for the total heat transfer in the system, which should be zero.

## Problem 19.61

A radiative heat transfer problem. To work out the temperature change approximate that all the heat is coming from the water and that the rate of heat output does not change during the cooling.

## Problem 19.72

A heat conduction problem.

## Problem 19.36

This problem involves the latent heat of vaporization of water (2260kJ/kg) and the first law of thermodynamics for an isobaric process.

To find $\Delta V$ you will need to consider the steam as an ideal gas, as we did when deriving the molar specific heat of an ideal gas at constant pressure.

Remember that the molecular mass of water is 18 g/mol.

## Problem 19.43

As we saw from the equipartition theorem an ideal diatomic gas should have a constant volume molar heat capacity of $c_{V,m}=\frac{5}{2}R$. Is this process constant volume or constant pressure?

Once you have decided on the appropriate molar heat capacity you will need to determine the number moles of gas. You can do this using the ideal gas law $PV=nRT$.

## Problem 19.54

You will need to use the result we obtained that for the quasistatic adiabatic expansion of an ideal gas that $PV^{\gamma}=\mathrm{constant}$ and that for any ideal gas $PV=nRT$.