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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
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Solution
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.
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