Heat Equations for Special Processes & Molar Specific Heats Practice Problems
A tube is filled with 0.150 moles of an ideal monoatomic gas with a pressure (initial) of 1.01 × 105 Pa. The initial volume of the gas is 0.00420 m3. The tube expands to a final volume that is three times the original volume. If the process is adiabatic, determine the final temperature (in K) and pressure.
A balloon of volume 0.00320 m3 contains an ideal gas at a pressure of 1.20 × 105 Pa. The number of moles in the ballon is 0.120. The balloon expands to 1.8 times the original volume. Calculate the final temperature (in K) and pressure assuming an isobaric process.
A container with a movable piston has 0.220 moles of helium. The initial pressure of helium is 1.01 × 105 Pa. The volume of the gas at this pressure is 0.00575 m3. The gas undergoes a process where the final volume is 1.5 times the initial volume. Determine the final temperature (in K) and pressure if the process is isothermal.
A hot air balloon contains air at a pressure equal to atmospheric pressure. A heater is used to raise the temperature of the air in the balloon to a temperature of 95.0°C at ground level (P = 1 atm). The balloon is allowed to rise in the atmosphere. The process taking place in the hot air as the balloon rises in the atmosphere can be considered adiabatic. Determine the temperature of the air in the balloon when the surrounding pressure is 0.75 atm. Treat air like an ideal gas with γ = 1.40. Ignore the effects of the balloon on the enclosed air.
A 0.120 m3 container is filled with an ideal diatomic gas at a pressure of 1.80 × 105 Pa. The gas is compressed adiabatically to a final volume of 0.0600 m3. Determine the ratio final to the initial temperature, (Tf/T0). Does the process heat or cool the gas?
Compressed air in a container fitted with a piston is used as a shock absorber. In one instant, the air is compressed to 75% of its initial volume as it absorbs the shock. The shock absorber initially contained inert N2 gas at a pressure of 4.50 atm and 25.0°C. The container is a cylinder of diameter 0.180 m and height 0.420 m. Determine the temperature of N2 at maximum compression if the process is adiabatic and N2 is an ideal gas.
Piston air compressors are devices used to compress air to high pressures for storage in tanks. The device takes in air at atmospheric pressure (1 atm) and 18.0 °C. The compression is very fast such that it is assumed adiabatic. If the final volume is 0.120 of the initial volume, and air behaves like an ideal gas with γ = 1.40, determine the temperature and pressure at this instant of the compression.
A sample of helium has an initial volume of 0.140 m3 and initial pressure of 2.45 × 105 Pa. It is compressed adiabatically to a final volume of 0.0700 m3. Calculate the final pressure. Treat helium like an ideal gas, helium is monoatomic.
A container fitted with a piston contains 6.50 moles of an ideal monoatomic gas. The original pressure and volume are 3.20 × 104 Pa and 0.850 m3 respectively. The gas is allowed to expand adiabatically, doing 1640 J of work. Calculate the final pressure following the expansion.
0.840 mol of an ideal gas with an initial pressure of 1.60 atm is taken through an isothermal process at 82.0°C. The volume is lowered to 40.0% of the original volume. Does heat flow between the gas and the surroundings occur? If yes, how much and in which direction (use positive sign if into the gas; negative sign if out of the gas)?
The volume of an ideal gas in a metallic container is reduced at a uniform temperature. In the process, the gas loses 560 J of heat to keep its temperature uniform. Determine the work done by the gas in the process.
Consider a cylinder that holds 0.50 moles of helium gas at a pressure of 3.0 atm. Calculate the rise in temperature if 75 J of heat energy is absorbed by the gas during the isochoric process.
Consider a system containing a helium gas that undergoes the process A→B→C as described in the figure below. Determine the heat needed or removed for i) process A→B and ii) process B→C
