The thermal capacity of 40 g of aluminium (specific heat `=0.2 cal//gm^(@)C`)

Options

A. `168 J//.^(@)C`
B. `672J//.^(@)C`
C. `840 J//.^(@)C`
D. `33.6 J//.^(@)C`

Answer

To find the thermal capacity of 40 g of aluminium with a specific heat capacity of 0.2 cal/g°C, we can follow these steps:

### Step 1: Understand the formula for thermal capacity
The thermal capacity (C) of a substance can be calculated using the formula:
\[ C = m \times s \]
where:
- \( C \) is the thermal capacity,
- \( m \) is the mass of the substance,
- \( s \) is the specific heat capacity.

### Step 2: Identify the given values
From the problem statement, we have:
- Mass (\( m \)) = 40 g
- Specific heat capacity (\( s \)) = 0.2 cal/g°C

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula:
\[ C = 40 \, \text{g} \times 0.2 \, \text{cal/g°C} \]

### Step 4: Calculate the thermal capacity in calories
Calculating the above expression:
\[ C = 40 \times 0.2 = 8 \, \text{cal/°C} \]

### Step 5: Convert calories to Joules
Since the problem requires the answer in Joules, we need to convert calories to Joules. We know that:
\[ 1 \, \text{cal} = 4.2 \, \text{J} \]
Thus, we can convert 8 calories to Joules:
\[ C = 8 \, \text{cal/°C} \times 4.2 \, \text{J/cal} = 33.6 \, \text{J/°C} \]

### Final Answer
The thermal capacity of 40 g of aluminium is:
\[ C = 33.6 \, \text{J/°C} \]

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