50 g of pure water is taken at `20^(@)`C. What is the amount of heat required to raise its temperature to `80^(@)`C?

Explanation

To solve the problem of calculating the amount of heat required to raise the temperature of 50 g of pure water from 20°C to 80°C, we can follow these steps:

### Step 1: Identify the given values
- Mass of water (m) = 50 g
- Initial temperature (T1) = 20°C
- Final temperature (T2) = 80°C
- Specific heat capacity of water (s) = 1 cal/g°C

### Step 2: Calculate the temperature difference (ΔT)
To find the temperature difference, we subtract the initial temperature from the final temperature:
\[ \Delta T = T2 - T1 = 80°C - 20°C = 60°C \]

### Step 3: Use the formula for heat (Q)
The formula to calculate the amount of heat required is:
\[ Q = m \cdot s \cdot \Delta T \]
where:
- Q = heat energy (in calories)
- m = mass of the substance (in grams)
- s = specific heat capacity (in cal/g°C)
- ΔT = change in temperature (in °C)

### Step 4: Substitute the values into the formula
Now, we can substitute the known values into the formula:
\[ Q = 50 \, \text{g} \cdot 1 \, \text{cal/g°C} \cdot 60 \, \text{°C} \]

### Step 5: Calculate the heat (Q)
Now, we perform the multiplication:
\[ Q = 50 \cdot 1 \cdot 60 = 3000 \, \text{calories} \]

### Step 6: Convert calories to kilocalories
Since 1 kilocalorie (kcal) = 1000 calories, we can convert the result:
\[ Q = \frac{3000 \, \text{cal}}{1000} = 3 \, \text{kcal} \]

### Final Answer
The amount of heat required to raise the temperature of 50 g of pure water from 20°C to 80°C is **3 kilocalories**.

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