22. The First Law of Thermodynamics

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.

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?

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?

A cylinder contains 0.100 mol of an ideal monatomic gas. Initially the gas is at $1.00\times {10}^5$ Pa and occupies a volume of $2.50\times {10}^{-3}$ m³. If the gas is allowed to expand to twice the initial volume, find the final temperature (in kelvins) and pressure of the gas if the expansion is (i) isothermal; (ii) isobaric; (iii) adiabatic.

On a warm summer day, a large mass of air (atmospheric pressure $1.01\times {10}^5$ Pa) is heated by the ground to $26.0$°C and then begins to rise through the cooler surrounding air. (This can be treated approximately as an adiabatic process; why?) Calculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only $0.850\times {10}^5$ Pa. Assume that air is an ideal gas, with $g=1.40$. (This rate of cooling for dry, rising air, corresponding to roughly $1$ C° per $100$ m of altitude, is called the dry adiabatic lapse rate.)

A player bounces a basketball on the floor, compressing it to $80.0\%$ of its original volume. The air (assume it is essentially N₂ gas) inside the ball is originally at $20.0$°C and $2.00$ atm. The ball's inside diameter is $23.9$ cm. What temperature does the air in the ball reach at its maximum compression? Assume the compression is adiabatic and treat the gas as ideal.

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.

A monatomic ideal gas that is initially at $1.50\times10^5$ Pa and has a volume of $0.0800$ m³ is compressed adiabatically to a volume of $0.0400$ m³. What is the ratio of the final temperature of the gas to its initial temperature? Is the gas heated or cooled by this compression?

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?

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?

During an isothermal compression of an ideal gas, $410$ J of heat must be removed from the gas to maintain constant temperature. How much work is done by the gas during the process?

A monatomic gas follows the process 1→2→3 shown in FIGURE EX19.26. How much heat is needed for (a) process 1→2 and (b) process 2→3?

A container holds 1.0 g of oxygen at a pressure of 8.0 atm. How much heat is required to increase the temperature by 100°C at constant pressure?

A container holds 1.0 g of oxygen at a pressure of 8.0 atm. How much will the temperature increase if this amount of heat energy is transferred to the gas at constant volume?