The ratio of specific to molar heat capacity of a body

Options

A. is a universal constant
B. depends on the mass of the body
C. depends on the molecular weight of the body
D. is dimensionless

Explanation

To solve the question regarding the ratio of specific heat capacity to molar heat capacity of a body, we will follow these steps:

### Step 1: Define Specific Heat Capacity
Specific heat capacity (C) is defined as the amount of heat required to raise the temperature of a unit mass of a substance by 1 Kelvin (or 1 degree Celsius). Mathematically, it can be expressed as:
\[ C = \frac{Q}{m \Delta T} \]
where \( Q \) is the heat added, \( m \) is the mass, and \( \Delta T \) is the change in temperature.

### Step 2: Define Molar Heat Capacity
Molar heat capacity (s) is defined as the amount of heat required to raise the temperature of one mole of a substance by 1 Kelvin (or 1 degree Celsius). It can be expressed as:
\[ s = \frac{Q}{n \Delta T} \]
where \( n \) is the number of moles.

### Step 3: Relate Moles to Mass
To relate the two heat capacities, we need to express the number of moles in terms of mass. The number of moles \( n \) can be calculated using the formula:
\[ n = \frac{m}{M} \]
where \( M \) is the molar mass of the substance.

### Step 4: Substitute Moles into Molar Heat Capacity
Substituting \( n \) into the equation for molar heat capacity gives:
\[ s = \frac{Q}{\left(\frac{m}{M}\right) \Delta T} = \frac{QM}{m \Delta T} \]

### Step 5: Find the Ratio of Specific Heat Capacity to Molar Heat Capacity
Now, we can find the ratio of specific heat capacity to molar heat capacity:
\[ \frac{C}{s} = \frac{C}{\frac{QM}{m \Delta T}} \]
Since both \( C \) and \( s \) involve \( Q \) and \( \Delta T \), we can simplify:
\[ \frac{C}{s} = \frac{m}{M} \]

### Step 6: Conclusion
Thus, the ratio of specific heat capacity to molar heat capacity is:
\[ \frac{C}{s} = \frac{m}{M} \]
This indicates that the ratio depends on the molecular weight (molar mass) of the body.

### Final Answer
The ratio of specific to molar heat capacity of a body depends on the molecular weight of the body.

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