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 mass of water
The mass of water (m) is given as 50 g.

### Step 2: Determine the specific heat capacity of water
The specific heat capacity (c) of water is known to be 1 calorie/g°C. This means that 1 gram of water requires 1 calorie of heat to raise its temperature by 1°C.

### Step 3: Calculate the temperature change
The initial temperature (T1) is 20°C, and the final temperature (T2) is 80°C. The change in temperature (ΔT) can be calculated as:
\[ \Delta T = T2 - T1 = 80°C - 20°C = 60°C \]

### Step 4: Calculate the total heat required
Using the formula for heat (Q), which is:
\[ Q = m \times c \times \Delta T \]
Substituting the values:
\[ Q = 50 \, \text{g} \times 1 \, \text{calorie/g°C} \times 60 \, \text{°C} \]
\[ Q = 50 \times 60 = 3000 \, \text{calories} \]

### Step 5: Convert calories to kilocalories
Since 1 kilocalorie (kcal) is equal to 1000 calories, we can convert the total heat required:
\[ Q = \frac{3000 \, \text{calories}}{1000} = 3 \, \text{kcal} \]

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

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