Chapter 10, Problem 24A

Interpretation Introduction

Interpretation:

The energy needed to warm 7.40 g of water by 55⁰C needs to be determined.

Concept Introduction:

Specific heat capacity is the amount of heat that is required to raise a temperature of 1 kg substance by 1⁰C.

The amount of heat is calculated by the formula,

  $\text{Q}=\text{m}\text{C}\text{Δ}\text{T}$

Where,

Q represents heat

m represents mass

ΔT represents difference in temperature

C represents specific heat capacity

Answer to Problem 24A

1701.26J energy is needed to warm 7.40 g of water by 55⁰C.

Explanation of Solution

Given information:

Heat (Q) = 526 J

Mass (m) = 7.40 g

Temperature(T) = 17⁰C

Calculation:

The calculation of specific heat capacity is shown below:

  $\begin{array}{c}\text{Q}=\text{m}\text{C}\text{Δ}\text{T}\end{array}$

 $\begin{array}{c}\text{526}\text{J}\text{=}\text{7}\text{.40}\text{g}\text{×}\text{C}\text{×}\text{17}{}^{\text{0}}\text{C}\end{array}$

  $\begin{array}{c}\text{C}\text{=}\text{4}\text{.18}{\text{Jg}}^{\text{-1}}{}^{\text{0}}{\text{C}}^{-\text{1}}\end{array}$

The calculation of energy is shown below:

  $\begin{array}{c}\text{Q}=\text{m}\text{C}\text{Δ}\text{T}\end{array}$

  $\begin{array}{c}\text{Q}\text{=}\text{7}\text{.40}\text{g}\text{×}\text{4}{\text{.18Jg}}^{\text{-1}}{}^{\text{0}}{\text{C}}^{\text{-1}}\text{×}\text{55}{}^{\text{0}}\text{C}\end{array}$

   $\begin{array}{c}\text{=}\text{1701}\text{.26}\text{J}\end{array}$

Conclusion

Thus, 1701.26J energy is needed to warm 7.40 g of water by 55⁰C.