The First Law Of Thermodynamics
An ideal monatomic gas contains 2.0 mol of atoms at an absolute temperature of 400 K. Calculate the internal energy of the gas. (R = 8.314 J/(mol·K))
A large iceberg at −5 °C and a small cup of boiling water at 100 °C are compared. Which statement about their internal energies is correct?
An ideal gas in a rigid sealed container is heated, receiving 620 J of energy. Determine the change in internal energy of the gas.
An ideal gas expands against a constant external pressure of 2.5 × 10⁵ Pa, increasing its volume by 4.0 × 10⁻³ m³. During the expansion, 1 200 J of energy is transferred into the gas by heating. Calculate the change in internal energy of the gas.
An ideal gas undergoes an isothermal expansion from volume V₁ to volume V₂. Which statement correctly describes the energy transfers during this process?
A piston compresses an ideal gas, decreasing its volume by 1.5 × 10⁻³ m³ at a constant pressure of 3.0 × 10⁵ Pa. No energy is transferred by heating or cooling during this process. Calculate the change in internal energy of the gas.
Two thermodynamic processes connect the same initial and final states on a PV diagram. Process 1 follows a straight line; Process 2 follows a curve that bows outward (away from the axes). Which statement is correct?
An engineer designs a perfectly insulated cylinder in which an ideal gas is rapidly compressed. She observes that the gas temperature rises significantly despite no heating. Which thermodynamic process best describes this, and why does the temperature increase?
A container holds 5.0 × 10²³ atoms of an ideal monatomic gas at 300 K. Calculate the internal energy of the gas. ($k_{\mathrm{B}}$ = 1.38 × 10⁻²³ J/K)
An ideal monatomic gas undergoes an isobaric expansion at a pressure of 2.0 × 10⁵ Pa, and the volume increases by 3.0 × 10⁻³ m³. Using Q = (5/2)PΔV, calculate the heat transferred to the gas.
During a certain process, an ideal gas has 800 J of work done on it while simultaneously losing 500 J of energy by cooling. What is the change in internal energy of the gas?
On a PV diagram, an ideal gas moves from state A (P = 3.0 × 10⁵ Pa, V = 2.0 × 10⁻³ m³) to state B (P = 3.0 × 10⁵ Pa, V = 5.0 × 10⁻³ m³) along a horizontal line. Which thermodynamic process is this, and what is the magnitude of work done by the gas?
A deep-sea diver ascends slowly, and the air in her buoyancy vest expands as external water pressure decreases. The expansion is slow enough that the air temperature stays equal to the surrounding water temperature throughout. Which statement correctly applies the first law to the air in the vest?
An ideal monatomic gas at 600 K has its absolute temperature reduced to 200 K. By what factor does the internal energy change?
An ideal gas undergoes a cyclic process, returning to its original state on a PV diagram. Which statement about the net change in internal energy over one complete cycle is correct?
An ideal monatomic gas at 2.0 × 10⁵ Pa occupies 1.0 × 10⁻² m³. It is first compressed at constant pressure to 4.0 × 10⁻³ m³, then heated at constant volume until the pressure reaches 5.0 × 10⁵ Pa. Calculate the total work done on the gas during this two-step process.
A gas is compressed in a cylinder and its volume decreases. A student claims that the work done on the gas is negative because “compression takes energy away from the gas.” Evaluate this claim.
A weather balloon rises through the atmosphere. As it ascends, the external pressure drops and the gas inside expands. The balloon material provides negligible insulation, and the expansion happens slowly. If the surrounding air temperature is constant at 250 K throughout the ascent, determine what happens to the temperature of the gas inside the balloon and justify your reasoning using the first law.