The specific heat capacity of a pure substance can be found by dividing the heat needed to change the temperature of a sample of the substance by the mass of the sample and by the change in temperature. The heat capacity of a certain substance has been measured to be [tex]$4.35 \frac{J}{ g \cdot{ }^{\circ} C }$[/tex]. Suppose [tex]$310. g$[/tex] of the substance are heated until the temperature of the sample has changed by [tex]$21.4^{\circ} C$[/tex]. Write an equation that will let you calculate the heat [tex]$Q$[/tex] that was needed for this temperature change. Your equation should contain only symbols. Be sure you define each symbol.
Your equation:
[tex]$Q=$[/tex]
Definitions of your symbols:
[tex]$\square$[/tex] [tex]$=21.4^{\circ} C$[/tex]
Answer (2)
Define the symbols: Q for heat, c for specific heat capacity, m for mass, and Δ T for the change in temperature.
Write the equation for specific heat capacity: c = m Δ T Q .
Rearrange the equation to solve for Q : Q = c ⋅ m ⋅ Δ T .
State the final equation and define all symbols: Q = c ⋅ m ⋅ Δ T , where Q is heat, c is specific heat capacity, m is mass, and Δ T = 21. 4 ∘ C .
Q = c ⋅ m ⋅ Δ T
Explanation
Understanding the Problem The problem states that the specific heat capacity of a substance is found by dividing the heat needed to change the temperature of a sample by the mass of the sample and the change in temperature. We are given the specific heat capacity, the mass, and the change in temperature. We need to write an equation to calculate the heat required for the temperature change using only symbols and define each symbol.
Defining the Symbols Let's define the symbols we will use:
Q = heat needed for the temperature change (in Joules) c = specific heat capacity (in g ∘ C J )
m = mass of the substance (in grams) Δ T = change in temperature (in ∘ C )
Writing the Equation The formula for specific heat capacity is:
c = m Δ T Q
We need to rearrange this formula to solve for Q :
Q = c ⋅ m ⋅ Δ T
Substituting the Values Now, let's substitute the given values and symbols into the equation:
Q = c ⋅ m ⋅ Δ T
Where:
c = 4.35 g ⋅ ∘ C J m = 310. g Δ T = 21. 4 ∘ C
Final Answer Therefore, the equation to calculate the heat Q is:
Q = c ⋅ m ⋅ Δ T
Definitions of the symbols:
Q = heat needed (in Joules) c = specific heat capacity (in g ⋅ ∘ C J )
m = mass of the substance (in grams) Δ T = 21. 4 ∘ C
Examples
Understanding specific heat capacity is crucial in many real-world applications. For instance, when designing engines, engineers need to know how much heat different materials can absorb before they start to degrade. Similarly, in cooking, different foods have different specific heat capacities, which affects how quickly they heat up. Knowing these properties allows for better control and efficiency in various processes, from industrial manufacturing to everyday cooking.
The equation to calculate the heat Q needed for a temperature change is Q = c × m × ΔT, where c is the specific heat capacity, m is the mass, and ΔT is the temperature change. In this case, the specific heat capacity is 4.35 J/(g·°C), mass is 310 g, and temperature change is 21.4 °C. By substituting these values into the equation, you can find the total heat energy Q in Joules.
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