# First Law of Thermodynamics Practice Problems

Real gases can approach the behavior of ideal gases under certain conditions. Helium is thought to be the closest to an ideal gas with γ = 1.660. Calculate the molar heat capacities i) C_{V} and ii) C_{p} of helium.

A heat engine contains two moles of an ideal gas confined in a cylinder with a moveable piston. Fuel combustion provides 873 J of heat that increases the gas temperature from 45 °C to 60 °C under constant pressure. The heated gas expands and does 249 J of work on the piston. Calculate the ratio of heat capacities (γ) for the gas.

A student heats a vessel enclosing argon gas. During this process, argon absorbs an amount Q_{0} of heat energy and expands at constant pressure. Find the percentage of heat energy involved in the expansion work of argon.

A car radiator is filled with pure water. The radiator cap keeps the pressure at 3.5 atm and pushes the boiling point of water to 140°C. At 3.5 atm, the heat of vaporization is 2.11 × 10^{6} J/kg. What would be the increase in the internal energy (ΔU) of water if 250 g of the steam were formed from water at this temperature and pressure? At 3.5 atm and 140 °C, the densities of water and steam are 928.5 kg/m^{3} and 1.93 kg/m^{3}, respectively.

A chef wants to reduce the cooking time by a few minutes. To succeed, he raises the pressure to 4 atm inside the cooker. At this pressure, the boiling point of water, the density of water, and the density of steam are 144 °C, 922.2 kg/m^{3}, and 2.163 kg/m^{3 }respectively. What is the work (W) done by 200 g of steam formed at 144 °C inside the cooker?

A sample of gas has its volume reduced isobarically from 3 L to 1 L inside a vertical cylinder with a movable piston at a pressure of 1.25 atm. The gas temperature decreases by 10 °C and its internal energy by 1000 J. What is the heat exchanged (Q) during the process if (i) the gas is ideal, or (ii) the gas is not ideal?

At a temperature of 30 °C, a rubber balloon is filled with 3 moles of helium. The balloon is left out in the sun to expand. Helium absorbs 1000 J of heat and does 800 J of work on the rubber. Determine the final temperature (T_{f}) of helium.

During a laboratory experiment, a student uses a piston-cylinder assembly initially containing 10 cm^{3} of an ideal gas. The cylinder is heated with an electric resistor to maintain constant pressure of the expanding gas. The net energy added to the gas by heat is 5 J and the pressure sensor inside the cylinder indicates a value of 3 × 10^{5} Pa. Find the work done by the gas if the volume of the cylinder is doubled.

A silicate container containing 289 g of air is sealed with a piston. The gas inside the container expands under isobaric conditions and produces 500 J of work. What would be the final temperature (T_{f}) of the gas if the initial temperature is 290 K? The molar mass of air is 28.9 g/mol.

A monoatomic gas with C_{v}= 3/2R initially at p_{0} and V_{0} undergoes a process Δp/Δv = 2p_{0}/V_{0} that ends at V_{f} = 2V_{0}. The rms speed at the initial and final point is related by v_{rms f} = 2.5v_{rms,0}. Calculate the heat absorbed/lost during this process, giving the result in p_{0}, and V_{0}.

Equal samples (0.25 mol) of an ideal diatomic gas are treated through the processes represented below. Determine the amount of heat required in each process.

Interpret the information contained in the equation below that was used to solve a certain problem:

50 J = −(0.0142 mol)(8.31 J/mol K)(T)Ln(1/5).

Turbo boost allows heat engines to take in air at pressures above atmospheric pressure. A 0.300 L cylinder takes in air at 1.60 atm and 25 °C and 650 J of work is done compressing the adiabatically. Find the final temperature and volume of the air in the cylinder.

A neon sample undergoes adiabatic expansion from V_{0} to 2V_{0}, where V_{0} is the initial volume. Will the mean free path increase/decrease, and by what factor? If not, give a reason.

At an initial pressure of 4.0 atm and a temperature of 200°C, 0.15 mol of N_{2} gas is present in a closed vessel. Following an adiabatic expansion process, the volume of the gas triples. Determine the final pressure of the nitrogen gas within the vessel.