What are the units for heat capacity?

What are the units for heat capacity?

• A. joules per degree Celsius
• B. joules per gram
• C. joules per kilogram per degree Celsius
• D. calories per degree Celsius

Answer: (A)

Heat capacity is defined as the amount of heat needed to raise the temperature of a system by one degree. Since it relates an amount of energy to a change in temperature, its unit must be energy per temperature. In SI units that’s joules per kelvin. Because a one-degree Celsius change is the same magnitude as a one-kelvin change, joules per degree Celsius is numerically identical to joules per kelvin. That’s why the option with joules per degree Celsius correctly represents heat capacity. The other options don’t fit the concept: joules per gram would be energy per mass (that’s a form of specific heat capacity, not total heat capacity); joules per kilogram per degree Celsius is also a per-mass quantity (specific heat capacity); calories per degree Celsius is a non-SI unit of energy per temperature (valid in some contexts, but SI practice uses joules).

Heat capacity is defined as the amount of heat needed to raise the temperature of a system by one degree. Since it relates an amount of energy to a change in temperature, its unit must be energy per temperature. In SI units that’s joules per kelvin. Because a one-degree Celsius change is the same magnitude as a one-kelvin change, joules per degree Celsius is numerically identical to joules per kelvin. That’s why the option with joules per degree Celsius correctly represents heat capacity.

The other options don’t fit the concept: joules per gram would be energy per mass (that’s a form of specific heat capacity, not total heat capacity); joules per kilogram per degree Celsius is also a per-mass quantity (specific heat capacity); calories per degree Celsius is a non-SI unit of energy per temperature (valid in some contexts, but SI practice uses joules).