How much heat is required to raise the temperature of 1 kg of water from 20°C to 70°C? (Specific heat 4200 J/kg°C)
A. 210,000 J
B. 252,000 J
C. 180,000 J
D. 50,000 J
Answer (2)
The heat required to raise the temperature of 1 kg of water from 20°C to 70°C is calculated to be 210,000 J. This is found using the specific heat formula Q = m c Δ T . Therefore, the correct option is A. 210,000 J.
;
Calculate the change in temperature: Δ T = 70° C − 20° C = 50° C .
Use the formula for heat transfer: Q = m c Δ T .
Substitute the given values: Q = ( 1 kg ) × ( 4200 J/kg°C ) × ( 50 °C ) .
Calculate the heat required: Q = 210 , 000 J . The final answer is 210 , 000 J .
Explanation
Problem Analysis We are asked to calculate the amount of heat required to raise the temperature of 1 kg of water from 20°C to 70°C, given the specific heat of water is 4200 J/kg°C.
Calculate the Change in Temperature First, we need to find the change in temperature, which is the final temperature minus the initial temperature: Δ T = T f − T i = 70° C − 20° C = 50° C
Calculate the Heat Required Next, we use the formula for heat transfer: Q = m c Δ T where:
Q is the heat required (in Joules),
m is the mass of the water (in kg),
c is the specific heat of water (in J/kg°C),
Δ T is the change in temperature (in °C). Plugging in the given values: Q = ( 1 kg ) × ( 4200 J/kg°C ) × ( 50 °C ) = 210 , 000 J
Final Answer Therefore, the amount of heat required to raise the temperature of 1 kg of water from 20°C to 70°C is 210,000 J.
Examples
This calculation is crucial in many real-world applications. For example, when designing a heating system for a building, engineers need to calculate the amount of energy required to heat water to a certain temperature. Similarly, in cooking, understanding the heat required to boil water or cook food is essential. This principle is also used in industrial processes where temperature control is vital for chemical reactions and material processing.
