How many calories are released when 500 g of water cools from 95.0°C to 25.0°C?
A. 4.75 x 104 cal
B. 1.25 x 104 cal
C. 70.0 cal
D. 35.0 cal
E. 3.50 x 104 cal
Answer (1)
Calculate the change in temperature: Δ T = 25.0° C − 95.0° C = − 70.0° C .
Use the formula Q = m c Δ T to calculate the heat released: Q = ( 500 g ) × ( 1 g ° C cal ) × ( − 70.0° C ) = − 35000 cal .
Take the absolute value to find the amount of heat released: ∣ Q ∣ = 35000 cal .
Express the answer in scientific notation: 3.50 × 1 0 4 cal .
Explanation
Understanding the Problem We are asked to calculate the amount of heat released when 500 g of water cools from 95.0°C to 25.0°C. We know that the specific heat of water is 1 cal/g°C. We can use the formula Q = m c Δ T , where Q is the heat released, m is the mass of water, c is the specific heat of water, and Δ T is the change in temperature.
Calculating the Change in Temperature First, we need to calculate the change in temperature, which is the final temperature minus the initial temperature: Δ T = T f − T i = 25.0° C − 95.0° C = − 70.0° C
Calculating the Heat Released Now, we can calculate the amount of heat released using the formula Q = m c Δ T : Q = ( 500 g ) × ( 1 g ° C cal ) × ( − 70.0° C ) = − 35000 cal Since we are looking for the amount of heat released , we take the absolute value of the result: ∣ Q ∣ = ∣ − 35000 cal ∣ = 35000 cal We can express this in scientific notation as 3.50 × 1 0 4 cal.
Final Answer Therefore, the amount of heat released when 500 g of water cools from 95.0°C to 25.0°C is 3.50 × 1 0 4 cal.
Examples
Imagine you're cooling down a pot of soup. This calculation helps determine how much energy the soup releases as it cools, which is crucial for designing efficient cooling systems or understanding energy transfer in cooking. Knowing the heat capacity of water and the temperature change allows us to quantify the heat released, similar to how engineers design cooling systems for engines or electronic devices. This principle is also fundamental in understanding climate change, where large bodies of water absorb and release heat, influencing global temperatures.
