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.

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.

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?

An experimenter adds $970$ J of heat to $1.75$ mol of an ideal gas to heat it from $10.0$°C to $25.0$°C at constant pressure. The gas does $+223$ J of work during the expansion. Calculate $\gamma$ for the gas.

Five moles of monatomic ideal gas have initial pressure $2.50\times {10}^3$ Pa and initial volume $2.10$ m³. While undergoing an adiabatic expansion, the gas does $1480$ J of work. What is the final pressure of the gas after the expansion?

The temperature of $0.150$ mol of an ideal gas is held constant at $77.0$°C while its volume is reduced to $25.0\%$ of its initial volume. The initial pressure of the gas is $1.25$ atm. Does the gas exchange heat with its surroundings? If so, how much? Does the gas absorb or liberate heat?

Heat $Q$ flows into a monatomic ideal gas, and the volume increases while the pressure is kept constant. What fraction of the heat energy is used to do the expansion work of the gas?