First Law of Thermodynamics Practice Problems

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 × 10⁶ 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/m³ and 1.93 kg/m³, 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/m³, and 2.163 kg/m³ 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 cm³ 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 × 10⁵ 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 container left in the sun contains 1.80 moles of an ideal gas at 68.0°C and 2.00 atm pressure. Calculate the work required to compress the gas to 1/4 of the initial volume while the pressure remains constant at 2.00 atm.

During an emergency stop, a 1100 kg truck is brought to rest from a speed of 85 km/h. How many joules and kilocalories are generated by the truck's braking system to achieve this stop?

A hockey puck with a mass of 0.16 kilograms slides across an ice rink at an initial speed of 25 m/s before coming to rest due to friction with the ice surface which is at 0°C and absorbs about half (50%) of all generated heat energy from frictional forces. How much ice does it melt?

An underwater researcher releases an oxygen bubble with a diameter of 5.0 cm from a depth of about 20.0 m beneath sea level. The temperature remains constant at around $25^{\circ} \mathrm{C}$. Assume that oxygen behaves like an ideal gas. What will be its diameter when it reaches sea level? Use density of seawater = $1025 \mathrm{~kg} / \mathrm{m}^{3}$ and atmospheric pressure = 101325 Pa.

An underwater researcher releases an oxygen bubble with a diameter of 5.0 cm from a depth of about 20.0 m beneath sea level. The temperature remains constant at around 25 °C. Assume that oxygen behaves like an ideal gas. Draw up PV diagrams for this process. Use density of seawater = 1025 kg/m3 and atmospheric pressure = 101325 Pa.

An underwater researcher releases an O₂ bubble with a diameter d₁ of 5.0 cm from a depth h of 20.0 m below sea level. The temperature T is constant at 25°C. Assume O₂ behaves like an ideal gas. The bubble's diameter at sea level d₂ is 7.2 cm. Using thermodynamics, determine:

i) Work done by O₂ during ascent;

ii) Change in internal energy;

iii) Whether heat was added or subtracted.

Use density of seawater $\rho$ = 1025 kg/m³ and atmospheric pressure P_atm = 101325 Pa.

A gas enclosed in a piston-container assembly loses 340 J of heat as it is compressed from 450 cm³ to 200 cm³ at constant pressure. The internal energy of the gas increases by 220 J. Calculate the pressure during the process.  

Imagine two vessels that contain 0.20 mol of a monoatomic gas that are at identical initial conditions of 400 K and 5 atm pressure. Vessel A undergoes an isothermal expansion, while vessel B undergoes an adiabatic expansion until they both reach a final pressure of 3 atm. What will be the final temperatures and volumes of this gas inside of each vessel?

Calculate the heat absorbed by a perfect gas that undergoes an isothermal expansion, performing 3.75 x 10³ J of work.

A pump is used to slowly compress, isothermally, 5.00 L of helium at 25°C and 1.50 atm to a volume of 3.00 L at the same temperature. How much work is done by the pump?

Using the ideal gas law, determine the amount of heat directed at the diatomic gas from points b to c as seen in the process shown below.