Ideal Gas Equation

The heat transfer through the plate is governed by Fourier's law of heat conduction: Where: - is the heat transferred per second (42 J), - is the thermal conductivity (which we need to find), - is the area of the cross-section of the plate (3750 cm = m ), - is the temperature difference between the two surfaces (14°C), - is the thickness of the plate (5 mm = 5 × 10 m). Rearranging the equation to solve for : Substitute the known values: Thus, the thermal conductivity of the metal is .

Let the length of the pipe be , and the speed of sound in air be . For the open pipe, the fundamental frequency is given by: For the closed pipe, the fundamental frequency is given by: The difference between the fundamental frequencies is given as 100 Hz: Now, the second harmonic frequency of the open pipe is: And the third harmonic frequency of the closed pipe is: The difference between and is: Thus, the difference is .

The average kinetic energy per molecule of a gas is given by: Where is the Boltzmann constant and is the temperature in Kelvin. Since the temperature is the same for both gases, the average kinetic energy per molecule depends only on the type of gas. The ratio of the average kinetic energies per molecule of hydrogen and nitrogen is: Thus, the ratio of the average kinetic energies per molecule of hydrogen and nitrogen is .