22. The First Law of Thermodynamics

n moles of an ideal gas at temperature T₁ and volume V₁ expand isothermally until the volume has doubled. In terms of n, T₁, and V₁, what is the final temperature?

The beaker in FIGURE P19.45, with a thin metal bottom, is filled with 20 g of water at 20°C. It is brought into good thermal contact with a 4000 cm³ container holding 0.40 mol of a monatomic gas at 10 atm pressure. Both containers are well insulated from their surroundings. What is the gas pressure after a long time has elapsed? You can assume that the containers themselves are nearly massless and do not affect the outcome.

Suppose 3.0 mol of neon (a monatomic gas, assume ideal) at STP are compressed slowly and isothermally to 0.22 the original volume. The gas is then allowed to expand quickly and adiabatically back to its original volume. Find the highest and lowest temperatures and pressures attained by the gas, and show on a PV diagram where these values occur.

In Problems 75, 76, and 77 you are given the equation used to solve a problem. For each of these, you are to write a realistic problem for which this is the correct equation.

$50\text{J}=-n\left(8.31\text{J/mol K}\right)\left(350\text{K}\right)\ln \left(\frac{1}{3}\right)(200\times {10}^{-6}{\text{m}}^3)(13,600{\text{kg/m}}^3)$

An ideal-gas process is described by p=cV^1/2, where c is a constant. 0.033 mol of gas at an initial temperature of 150°C is compressed, using this process, from 300 cm³ to 200 cm³. How much work is done on the gas?

A monatomic gas is adiabatically compressed to 1/8 of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not? The molar specific heat at constant volume.

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. What are the gas volume and temperature after the expansion?

n moles of an ideal gas at temperature T₁ and volume V₁ expand isothermally until the volume has doubled. In terms of n, T₁, and V₁, what are the heat energy transferred to the gas?

A gas cylinder holds 0.10 mol of O₂ at 150°C and a pressure of 3.0 atm. The gas expands adiabatically until the volume is doubled. What are the final pressure?

The engine of a Ferrari F355 F1 sports car takes in air at $20.0$°C and $1.00$ atm and compresses it adiabatically to $0.0900$ times the original volume. The air may be treated as an ideal gas with $g=1.40$. Find the final temperature and pressure.

5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. What is the gas pressure after the decrease?

An experiment you're designing needs a gas with γ = 1.50. You recall from your physics class that no individual gas has this value, but it occurs to you that you could produce a gas with γ = 1.50 by mixing together a monatomic gas and a diatomic gas. What fraction of the molecules need to be monatomic?

How much heat energy is needed to increase the temperature of 5 mol of an ideal diatomic gas by from 273K to 300K if the a) pressure is held constant; b) the volume is held constant?

A monatomic gas is adiabatically compressed to 1/8 of its initial volume. Does each of the following quantities change? If so, does it increase or decrease, and by what factor? If not, why not? The thermal energy of the gas.

n moles of an ideal gas at temperature T₁ and volume V₁ expand isothermally until the volume has doubled. In terms of n, T₁, and V₁, what are the work done on the gas?