Question

The ratio of specific heat capacity to molar heat capacity of a body _____________ .

Options

• is a universal constant

• depends on the mass of the body

• depends of the molecular weight of the body

• is dimensionless

Answer 1

depends of the molecular weight of the body

 

Specific heat capacity of a body,

\[s = \frac{Q}{m\Delta\theta}\]

Here,

Q = Heat supplied

m = Mass of body

Δθ = Change in temperature

Molar heat capacity of a body,

\[C = \frac{Q}{n\Delta\theta}\]

Here,

Q = Heat supplied

n = Number of moles

Δθ = Change in temperature

∴ The ratio of the specific heat capacity and molar heat capacity is given by

\[\frac{s}{C} = \frac{\frac{Q}{m\Delta\theta}}{\frac{Q}{n\Delta\theta}} = \frac{n}{m} = \frac{n}{nM} = \frac{1}{M}\]

Here,

M = Molar mass related to number of moles

m = Mass

As the value of M is different for different bodies of different composition, the ratio cannot be a universal constant.

Also, the ratio is independent of the mass of the body.
The ratio of the specific heat and molar heat capacity depends on the molecular weight of the body.

Clearly, the unit of molecular weight is kg/mole. So, the ratio that depends only on the molecular weight cannot be dimensionless.