Questions: Increasing the temperature of 50 grams of water by 1°C requires how many calories?

Solution Steps

The specific heat capacity of water is defined as the amount of heat required to raise the temperature of 1 gram of water by \(1^{\circ} \mathrm{C}\). This value is known to be 1 calorie per gram per degree Celsius.

Given that we have 50 grams of water, we need to calculate the total heat required to raise the temperature of this amount of water by \(1^{\circ} \mathrm{C}\). Using the specific heat capacity, we can determine this as follows: \[ \text{Heat required} = \text{mass} \times \text{specific heat capacity} \times \Delta T \] where:

• \(\text{mass} = 50 \, \text{grams}\)
• \(\text{specific heat capacity} = 1 \, \text{calorie/gram/}^{\circ} \mathrm{C}\)
• \(\Delta T = 1^{\circ} \mathrm{C}\)

Substituting the values into the formula, we get: \[ \text{Heat required} = 50 \, \text{grams} \times 1 \, \text{calorie/gram/}^{\circ} \mathrm{C} \times 1^{\circ} \mathrm{C} = 50 \, \text{calories} \]

Final Answer