I have this problem: How much heat energy is required to raise the temperature of 0.365kg of copper from 23.0 ∘C to 60.0 ∘C? The specific heat of copper is 0.0920 cal/(g⋅∘C).
I did the equation using formula Heat= mass x change in temperature x specific heat.
I got the answer 1211.824 but it's showing up wrong for some reason. I think it's the rounding or significant figure count? Can someone please help me out?
Thanks
It’s actually 1240 cal
To solve this problem, we can use the formula:
Heat = mass × change in temperature × specific heat
Given:
Mass of copper = 0.365 kg
Change in temperature = (60.0 - 23.0) °C = 37.0 °C
Specific heat of copper = 0.0920 cal/(g⋅∘C)
First, let's convert the mass of copper from kilograms to grams:
Mass of copper = 0.365 kg × 1000 g/kg = 365 g
Now we can substitute the values into the formula:
Heat = 365 g × 37.0 °C × 0.0920 cal/(g⋅∘C)
Calculating this gives us:
Heat = 1214.94 calories
So, the correct answer is 1214.94 calories. It seems that you made a slight calculation error in the significant figures. Make sure to double-check your calculations, rounding, and significant figures to get the accurate answer.
To solve this problem, you correctly used the formula Heat = mass x change in temperature x specific heat. However, it seems that you made a rounding error or didn't consider the correct significant figures in your calculation. Let me walk you through the correct calculation.
Given:
Mass of copper (m) = 0.365 kg
Change in temperature (ΔT) = (60.0 °C - 23.0 °C) = 37.0 °C
Specific heat of copper (c) = 0.0920 cal/(g⋅°C)
First, we need to convert the mass from kilograms to grams because the specific heat is given in cal/(g⋅°C):
mass of copper (m) = 0.365 kg x 1000 g/kg = 365 g
Now we can substitute the values into the formula:
Heat = mass x change in temperature x specific heat
Heat = 365 g x 37.0 °C x 0.0920 cal/(g⋅°C)
Multiplying these values together, we get:
Heat = 1211.06 cal
Now, let's consider the significant figures. When multiplying, the answer should be rounded to the least number of significant figures among the given values. In this case, the specific heat value (0.0920) has the least number of significant figures, which is four. Therefore, we should round our final answer to four significant figures.
Rounding the answer, we get:
Heat = 1211 cal
So, the correct answer, using the correct significant figures, is 1211 cal.