To find the speed of sound, what unit should the specific gas constant be in?

The speed of sound in a gas is determined using the equation derived from the ideal gas law and thermodynamics. Specifically, the speed of sound ( c ) in a gas can be expressed as:

[ c = \sqrt{\frac{\gamma R T}{M}} ]

where ( \gamma ) is the adiabatic index (ratio of specific heats), ( R ) is the specific gas constant, ( T ) is the absolute temperature in Kelvin, and ( M ) is the molar mass of the gas.

In this equation, the specific gas constant ( R ) must have units that make the equation dimensionally consistent. The units of ( R ) are typically expressed as Joules per kilogram per Kelvin (J/kg·K). This reflects the energy per unit mass and temperature change, which is essential for calculating the energy dynamics associated with sound propagation in the gas.

Thus, the specific gas constant must be in Joules per kilogram per Kelvin to appropriately relate temperature changes to energy per unit mass, allowing for an accurate calculation of the speed of sound. This ensures that when substituting values into the equation, the units work out correctly to give a speed (usually expressed in meters per second).