Question

The amount of heat needed to change the temperature of an object can be calculated using the following equation: q = m c subscript p δt where q = amount of heat in calories m = mass of object in grams c subscript p = specific heat of object δt = change in temperature in c to the power of 0 what is the appropriate unit for p c if the preceding equation is to be homogeneous in units?

Answer 1

The appropriate unit for specific heat (cp) to maintain homogeneous units in the equation q = mcpΔt is calories per gram per degree Celsius (cal/g°C) or joules per kilogram per degree Celsius (J/kg°C) when using SI units.

Step-by-step explanation:

The appropriate unit for specific heat (cp) in the equation q = mcpΔt to be homogeneous in units is calories per gram per degree Celsius (cal/g°C) or alternatively, joules per kilogram per degree Celsius (J/kg°C) when using SI units. Consequently, if the heat (q) is measured in calories, specific heat must also be in terms of calories to maintain consistency in units within the equation.

As the equation is q = m × cp × Δt, the q is the amount of heat typically measured in calories or joules, m is mass in grams or kilograms, cp is the specific heat, and Δt is the temperature change in degrees Celsius. For the units to be homogeneous, or consistent, across the equation when determining the amount of heat transfer needed to change the temperature of an object, the units of specific heat (c) must match the units of heat (q) per unit mass per unit temperature change.