Back(II) The pressure in an ideal gas is cut in half slowly, while being kept in a container with rigid walls. In the process, 425 kJ of heat left the gas. (a) How much work was done during this process? (b) What was the change in internal energy of the gas during this process?
An audience of 1600 fills a concert hall of volume 22,000 m3. If there were no ventilation, by how much would the temperature of the air rise over a period of 2.0 h due to the metabolism of the people (70 W/person)?
(II) A 2.00-mole sample of N₂ gas at 0°C is heated to 150°C at constant pressure (1.00 atm). Determine (a) the change in internal energy, (b) the work the gas does, and (c) the heat added to it.
(II) Show that the work done by n moles of an ideal gas when it expands adiabatically is W = nCv( T₁ - T₂) , where T₁ and T₂ are the initial and final temperatures, and Cv is the molar specific heat at constant volume.
A bicycle pump is a cylinder 22 cm long and 3.0 cm in diameter. The pump contains air at 20.0°C and 1.0 atm. If the outlet at the base of the pump is blocked and the handle is pushed in very quickly, compressing the air to half its original volume, how hot does the air in the pump become?
A diesel engine accomplishes ignition without a spark plug by an adiabatic compression of air to a temperature above the ignition temperature of the diesel fuel, which is injected into the cylinder at the peak of the compression. Suppose air is taken into the cylinder at 280 K and volume V₁ and is compressed adiabatically to 560° C ( ≈ 1000 °F) and volume V₂. Assuming that the air behaves as an ideal gas whose ratio of CP to CV is 1.4, calculate the compression ratio V₁/ V₂ of the engine.
Show, using Eqs. 19–7 and 19–16, that the work done by a gas that slowly expands adiabatically from pressure P₁ and volume V₁ , to P₂ and V₂, is given by W = (P₁V₁ - P₂V₂) / (γ - 1).
Consider the following two-step process. Heat is allowed to flow out of an ideal gas at constant volume so that its pressure drops from 2.2 atm to 1.4 atm. Then the gas expands at constant pressure, from a volume of 5.9 L to 9.3 L, where the temperature reaches its original value. Calculate (a) the total work done by the gas in the process, (b) the change in internal energy of the gas in the process, and (c) the total heat flow into or out of the gas.
At very low temperatures, the molar specific heat of many substances varies as the cube of the absolute temperature: C = k (T3 / T30) which is sometimes called Debye’s law. For rock salt, T0 = 281 K and k = 1940 J/mol · K. Determine the heat needed to raise 2.75 mol of salt from 22.0 K to 46.0 K.
Suppose 3.0 mol of neon (a monatomic gas, assume ideal) at STP are compressed slowly and isothermally to 0.22 the original volume. The gas is then allowed to expand quickly and adiabatically back to its original volume. Find the highest and lowest temperatures and pressures attained by the gas, and show on a PV diagram where these values occur.
The beaker in FIGURE P19.45, with a thin metal bottom, is filled with 20 g of water at 20°C. It is brought into good thermal contact with a 4000 cm3 container holding 0.40 mol of a monatomic gas at 10 atm pressure. Both containers are well insulated from their surroundings. What is the gas pressure after a long time has elapsed? You can assume that the containers themselves are nearly massless and do not affect the outcome.
A 100 cm³ box contains helium at a pressure of 2.0 atm and a temperature of 100℃. It is placed in thermal contact with a 200 cm³ box containing argon at a pressure of 4.0 atm and a temperature of 400℃. How much heat energy is transferred, and in which direction?
Propane gas (C3H8) behaves like an ideal gas with . Determine the molar heat capacity at constant volume and the molar heat capacity at constant pressure.
An experimenter adds J of heat to mol of an ideal gas to heat it from °C to °C at constant pressure. The gas does J of work during the expansion. Calculate for the gas.
Heat 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?