Resnick & Halliday Solutions for Chapter: The Kinetic Theory of Gases, Exercise 1: Problems

Assume $10.0 \mathrm{g}$ of oxygen $\left({\mathrm{O}}_2\right)$ gas is heated at constant atmospheric pressure from $25.0°\mathrm{C}$ to$125°\mathrm{C}$. (a) How many moles of oxygen are present? (b) How much energy is transferred to the oxygen as heat? (The molecules rotate, but do not oscillate.) (c) What fraction of the heat is used to raise the internal energy of the oxygen?

The given figure shows two paths that may be taken by a gas from an initial point $i$ to a final point $f$. Path $1$ consists of an isothermal expansion (work is $60 \mathrm{J}$ in magnitude), an adiabatic expansion (work is $45 \mathrm{J}$in magnitude), an isothermal compression (work is $30 \mathrm{J}$ in magnitude), and then an adiabatic compression (work is $25 \mathrm{J}$ in magnitude). What is the change in the internal energy of the gas if the gas goes from point $i$ to point $f$ along path $2?$

An ideal diatomic gas, with rotation but no oscillation undergoes an adiabatic compression. Its initial pressure and volume are $1.20$ atm and $0.200 {\mathrm{m}}^3.$ Its final pressure is $3.60 \mathrm{atm}$. How much work is done by the gas?

A certain gas occupies a volume of $0.76 \mathrm{L}$ at a pressure of $1.2 \mathrm{atm}$ and a temperature of $4000 \mathrm{K}$. It is expanded adiabatically to a volume of $4.3 \mathrm{L}$. Determine
(a) the final pressure and
(b) the final temperature, assuming the gas to be an ideal gas for which $\gamma =1.4$.

The most probable speed of the molecules in a gas at temperature $T_2$ is equal to the average speed of the molecules at the temperature $T_1$. Find $\frac{T_2}{T_1}$.

The volume of an ideal gas is adiabatically reduced from $350 \mathrm{L}$ to $130 \mathrm{L}$. The initial pressure and temperature are $2.00 \mathrm{atm}$ and $380 \mathrm{K}$. The final pressure is $8.00 \mathrm{atm}$.

(a) Is the gas monatomic, diatomic or polyatomic?
(b) What is the final temperature?
(c) How many moles are in the gas?

Ginen:-$\log \left(35\right)=1.544 \text{and }\log \left(13\right)=1.114$

Under constant pressure, the temperature of $3.00 \mathrm{mol}$ of an ideal monatomic gas is raised $15.0 \mathrm{K}$. What are $\left(a\right)$ the work done $W$ by the gas, $\left(b\right)$ the energy transferred as heat $Q$, $\left(c\right)$ the change $\mathrm{\Delta }{E}_{\text{int }}$ in the internal energy of the gas and $\left(d\right)$ the change in average kinetic energy $\mathrm{\Delta }K$ per atom?

An automobile tyre has a volume of $1.64\times {10}^{-2} {\mathrm{m}}^3$ and contains air at a gauge pressure (pressure above atmospheric pressure) of $165 \mathrm{kPa}$, when the temperature is $0.00 °\mathrm{C}$. What is the gauge pressure of the air in the tyres when its temperature rises to $37.0 °\mathrm{C}$ and its volume increases to $1.67\times {10}^{-2} {\mathrm{m}}^3$? Assume the atmospheric pressure is $1.01\times {10}^5 \mathrm{Pa}$.