22. The First Law of Thermodynamics

0.10 mol of nitrogen gas follow the two processes shown in FIGURE P19.58. How much heat is required for each?

(II) The pressure in an ideal gas is cut in half slowly, while being kept in a container with rigid walls. In the process, 425 kJ of heat left the gas. (a) How much work was done during this process? (b) What was the change in internal energy of the gas during this process?

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 amount of heat energy is transferred from the gas as its pressure decreases?

Adiabatic temperature changes result from which of the following conditions in the atmosphere?

Consider the following two-step process. Heat is allowed to flow out of an ideal gas at constant volume so that its pressure drops from 2.2 atm to 1.4 atm. Then the gas expands at constant pressure, from a volume of 5.9 L to 9.3 L, where the temperature reaches its original value. Calculate (a) the total work done by the gas in the process, (b) the change in internal energy of the gas in the process, and (c) the total heat flow into or out of the gas.

Propane gas (C₃H₈) behaves like an ideal gas with $g=1.127$. Determine the molar heat capacity at constant volume and the molar heat capacity at constant pressure.

n moles of a diatomic gas with C_v = 5/2 R has initial pressure p_i and volume V_i. The gas undergoes a process in which the pressure is directly proportional to the volume until the rms speed of the molecules has doubled. How much heat does this process require? Give your answer in terms of n, p_i and V_i.

14 g of nitrogen gas at STP are adiabatically compressed to a pressure of 20 atm. What is the compression ratio V_max/V_min?

A cylinder contains $0.0100$ mol of helium at $T = 27.0$°C. If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from $27.0$°C to $67.0$°C? Draw a $pV$-diagram for this process.

An audience of 1600 fills a concert hall of volume 22,000 m³. If there were no ventilation, by how much would the temperature of the air rise over a period of 2.0 h due to the metabolism of the people (70 W/person)?

A cylinder contains $0.0100$ mol of helium at $T = 27.0$°C. If the gas is ideal, what is the change in its internal energy in part (a)? In part (b)? How do the two answers compare? Why?

(a) How much heat is needed to raise the temperature to $67.0$°C while keeping the volume constant? Draw a $pV$-diagram for this process.

(b) If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from $27.0$°C to $67.0$°C? Draw a $pV$-diagram for this process.

One cylinder in the diesel engine of a truck has an initial volume of 600 cm³. Air is admitted to the cylinder at 30°C and a pressure of 1.0 atm. The piston rod then does 400 J of work to rapidly compress the air. What are its final temperature and volume?

Show, using Eqs. 19–7 and 19–16, that the work done by a gas that slowly expands adiabatically from pressure P₁ and volume V₁ , to P₂ and V₂, is given by W = (P₁V₁ - P₂V₂) / (γ - 1).

A monatomic ideal gas that is initially at $1.50\times {10}^5$ Pa and has a volume of $0.0800$ m³ is compressed adiabatically to a volume of $0.0400$ m³. What is the final pressure?