Math Problem Statement

What is the heat required to raise the temperature of a 1.5 kg mass by 120°C if the specific heat of the mass is 0.37 cal./g. °C?

Solution

To find the heat required, we can use the formula:

Q=mcΔTQ = mc\Delta T

where:

  • QQ is the heat energy required,
  • mm is the mass of the object,
  • cc is the specific heat capacity of the material,
  • ΔT\Delta T is the change in temperature.

Let's plug in the given values:

  • m=1.5kg=1500gm = 1.5 \, \text{kg} = 1500 \, \text{g} (since 1 kg = 1000 g),
  • c=0.37cal/g°Cc = 0.37 \, \text{cal/g°C},
  • ΔT=120°C\Delta T = 120 \, \text{°C}.

Now calculate the heat QQ:

Q=(1500g)×(0.37cal/g°C)×(120°C)Q = (1500 \, \text{g}) \times (0.37 \, \text{cal/g°C}) \times (120 \, \text{°C})

Q=1500×0.37×120Q = 1500 \times 0.37 \times 120

Q=66,600calQ = 66,600 \, \text{cal}

So, the heat required to raise the temperature is 66,600 calories.

Would you like more details or have any questions about this calculation?

Here are five related questions you might find interesting:

  1. How would the heat required change if the mass were doubled?
  2. What happens to the heat required if the specific heat capacity changes to 0.50 cal/g°C?
  3. How much heat is required if the temperature change is only 60°C?
  4. What is the specific heat in joules if 1 cal = 4.184 J?
  5. How would the heat calculation differ if the mass was given in pounds instead of kilograms?

Tip: Always make sure to convert units consistently when performing calculations in different systems (e.g., grams vs kilograms).