Question

How much heat is required to raise the temperature of \( 2 \, \text{kg} \) of water from \( 25^\circ C \) to \( 75^\circ C \)? (Specific heat capacity of water \( c = 4200 \, \text{J/kg}^\circ C \))

• A. \( 4.2 \times 10^5 \, \text{J} \)
• B. \( 5.0 \times 10^5 \, \text{J} \)
• C. \( 3.5 \times 10^5 \, \text{J} \)
• D. \( 4.8 \times 10^5 \, \text{J} \)

Hint:

Heat required \( Q = mc\Delta T \), where \( m \) is mass, \( c \) specific heat, and \( \Delta T \) temperature change.

Answer 1

The Correct Option is A

The heat energy necessary to increase water temperature is calculated using the formula for heat transfer:

\( Q = mc\Delta T \)

where:

• \( Q \) is the heat energy (Joules)
• \( m \) is the water mass (kilograms)
• \( c \) is the specific heat capacity (J/kg°C)
• \( \Delta T \) is the temperature change (°C)

Problem details:

• \( m = 2 \, \text{kg} \)
• \( c = 4200 \, \text{J/kg}^\circ C \)
• Initial temperature = \( 25^\circ C \)
• Final temperature = \( 75^\circ C \)

The temperature change is calculated first:

\( \Delta T = 75^\circ C - 25^\circ C = 50^\circ C \)

Substituting the provided values into the heat transfer formula:

\( Q = 2 \times 4200 \times 50 \)

\( Q = 4200 \times 100 \)

\( Q = 420000 \, \text{J} \)

The required heat energy is \( 4.2 \times 10^5 \, \text{J} \).