A "flow calorimeter" is used to measure the specific heat of a liquid. Heat is added at a known rate to a stream of the liquid as it passes through the calorimeter at known rate, then a measurement of the resulting temperature difference between the in flow and the out flow points of the liquid stream enables us to compute the specific heat of the liquid. A liquid of density 0.85 `g//cm^(3)` flows through a calorimeter at the rate of 8.0 `cm^(3)//s`. heat is added by means of a 250 watt electric heating coil, and a temperature difference of `15^(@)C` is established in steady state conditions between the in flow and out flow points.
Q. Rate of heat absorption per unit specific heat capacity is

Options

A. 100g-`.^(@)C//s`
B. 102g-`.^(@)C//s`
C. 50g-`.^(@)C//s`
D. `10.2g-.^(@)C//s`

Answer

To solve the problem of finding the rate of heat absorption per unit specific heat capacity using the given data, we can follow these steps:

### Step 1: Understand the given data
We have the following information:
- Density of the liquid, \( \rho = 0.85 \, \text{g/cm}^3 \)
- Volume flow rate, \( V = 8.0 \, \text{cm}^3/\text{s} \)
- Power of the heating coil, \( P = 250 \, \text{W} \)
- Temperature difference, \( \Delta T = 15 \, \text{°C} \)

### Step 2: Convert power from watts to calories
Since 1 watt = 0.239 calories per second, we can convert the power:
\[ P = 250 \, \text{W} = 250 \times 0.239 \, \text{cal/s} = 59.75 \, \text{cal/s} \]

### Step 3: Calculate the mass flow rate
The mass flow rate \( \dot{m} \) can be calculated using the formula:
\[ \dot{m} = \rho \times V \]
Substituting the values:
\[ \dot{m} = 0.85 \, \text{g/cm}^3 \times 8.0 \, \text{cm}^3/\text{s} = 6.8 \, \text{g/s} \]

### Step 4: Use the heat transfer equation
The heat added to the liquid can also be expressed as:
\[ P = \dot{m} \cdot C \cdot \Delta T \]
Where \( C \) is the specific heat capacity. Rearranging this gives:
\[ C = \frac{P}{\dot{m} \cdot \Delta T} \]

### Step 5: Substitute the known values to find \( C \)
Substituting the values we have:
\[ C = \frac{59.75 \, \text{cal/s}}{6.8 \, \text{g/s} \cdot 15 \, \text{°C}} = \frac{59.75}{102} \approx 0.585 \, \text{cal/g°C} \]

### Step 6: Calculate the rate of heat absorption per unit specific heat capacity
The rate of heat absorption per unit specific heat capacity can be calculated as:
\[ \text{Rate of heat absorption per unit specific heat capacity} = \frac{P}{C} \]
Substituting the values:
\[ \text{Rate} = \frac{59.75 \, \text{cal/s}}{0.585 \, \text{cal/g°C}} \approx 102 \, \text{g°C/s} \]

### Final Answer
Thus, the rate of heat absorption per unit specific heat capacity is approximately:
\[ \text{Rate} \approx 102 \, \text{g°C/s} \]

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