Course: 17.7 特定热量计算

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特定热量计算
Does water have a high capacity for absorbing heat?
::水是否具有高吸收热量的能力?

Yes. In a car radiator, it serves to keep the engine cooler than it would otherwise run. (In the picture above, the radiator is the black object on the left.) As the water circulates through the engine, it absorbs from the engine block. When it passes through the radiator, the cooling fan and the exposure to the outside environment allow the water to cool somewhat before it makes another passage through the engine.
::是的,在汽车散热器中,它的作用是保持发动机的冷却,而不是它本来会运行的。 (在上图中,散热器是左边的黑色物体。 )当水通过发动机循环时,它从发动机块吸收。当它通过散热器时,冷却扇和对外部环境的接触使水在通过发动机的另外一条通道前有些冷却。

Specific Heat Calculations
::特定热量计算

The specific heat of a substance can be used to calculate the temperature change that a given substance will undergo when it is either heated or cooled. The equation that relates heat $\begin{align*}(q)\end{align*}$ to specific heat $\begin{align*}(c_p)\end{align*}$ , mass $\begin{align*}(m)\end{align*}$ , and temperature change $\begin{align*} (\Delta{T})\end{align*}$ is shown below.
::物质的具体热量可用于计算某一物质在加热或冷却时将经历的温度变化。以下列出了与特定热量(cp)、质量(m)和温度变化(T)有关的热量(q)的方程式。

$\begin{aligned} q = c_{p} \times m \times Δ T \end{aligned}$
$\begin{align*}q=c_p \times m \times \Delta{T} \end{align*}$
::q=cpxmT

The heat that is either absorbed or released is measured in joules. The mass is measured in grams. The change in temperature is given by $\begin{align*}\Delta{T}= T_f - T_i\end{align*}$ , where $\begin{align*}T_f\end{align*}$ is the final temperature and $\begin{align*}T_i\end{align*}$ is the initial temperature.
::吸收或释放的热用焦耳测量。质量用克测量。温度变化由 T=Tf-Ti 给出, Tf 是最后温度, Ti 是初始温度。

Sample Problem: Calculating Specific Heat
::样本问题:计算特定热量

A 15.0 g piece of cadmium metal absorbs 134 J of heat while rising from 24.0°C to 62.7°C. Calculate the specific heat of cadmium.
::一种15.0克镉金属吸收134焦热,同时从24.0摄氏度上升至62.7摄氏度。计算镉的具体热量。

Step 1: List the known quantities and plan the problem .
::第1步:列出已知数量并规划问题。

Known
::已知已知

heat = $\begin{align*}q\end{align*}$ = 134 J
::热量=q = 134 J

mass = $\begin{align*}m\end{align*}$ = 15.0 g
::质量 = m = 15.0克

$\begin{align*}\Delta{\text{T}} = 62.7^\circ \text{C} - 24.0^\circ \text{C} = 38.7^\circ \text{C}\end{align*}$
::T=62.7C-24.0C=38.7C

Unknown
::未知

$\begin{align*}c_p \ \text{of cadmium}= ? \ \text{J}/ \text{g}^\circ \text{C} \\\end{align*}$
::镉的 cp=? J/gC

The specific heat equation can be rearranged to solve for the specific heat.
::特定的热方程式可以重新排列,以解答特定的热量。

Step 2: Solve .
::步骤2:解决。

$\begin{aligned} c_{p} = \frac{q}{m \times Δ T} = \frac{134 J}{15.0 g \times {38.7}^{\circ} C} = 0.231 {J/g}^{\circ} C \end{aligned}$
$\begin{align*}c_p=\frac{q}{m \times \Delta{T}}=\frac{134 \text{ J}}{15.0 \text{ g} \times 38.7^\circ \text{C}}=0.231 \text{ J/g}^\circ \text{C}\end{align*}$
::cp=qmT=134 J15.0 g×38.7C=0.231 J/gC

Step 3: Think about your result .
::步骤3:想想你的结果。

The specific heat of cadmium, a metal, is fairly close to the specific heats of other . The result has three .
::镉是金属,其特定热量与其它金属的热量相当接近。结果为三。

Since most specific heats are known, they can be used to determine the final temperature attained by a substance when it is either heated or cooled. Suppose that a 60.0 g sample of water at 23.52°C was cooled by the removal of 813 J of heat. The change in temperature can be calculated using the specific heat equation.
::由于大多数特定热是已知的,因此这些热可以用来确定一种物质在加热或冷却时所达到的最后温度。假设23.52°C时的60.0克水样本通过去除813焦热而冷却。温度的变化可以使用特定的热方程式计算。

$\begin{aligned} Δ T = \frac{q}{c_{p} \times m} = \frac{813 J}{4.18 {J/g}^{\circ} C \times 60.0 g} = {3.24}^{\circ} C \end{aligned}$
$\begin{align*}\Delta{T}=\frac{q}{c_p \times m}=\frac{813 \text{ J}}{4.18 \text{ J/g}^\circ \text{C} \times 60.0 \text{ g}}=3.24^\circ \text{C} \end{align*}$
::T=qcp-m=813 J4.18 J/gC×60.0 g=3.24C

Since the water was being cooled, the temperature decreases. The final temperature is:
::自从水被冷却,温度下降。最后的温度是:

$\begin{aligned} T_{f} = {23.52}^{\circ} C - {3.24}^{\circ} C = {20.28}^{\circ} C \end{aligned}$
$\begin{align*}T_f=23.52^\circ \text{C} - 3.24^\circ \text{C}=20.28^\circ \text{C}\end{align*}$
::Tf=23.52C-3.24C=20.28C

Summary
::摘要

Specific heat calculations are illustrated.
::具体说明了具体的热计算。

Review
::回顾

Do different materials have different specific heats?
::不同材料有不同特定的热量吗?

How does mass affect heat absorbed?
::质量如何影响热吸收?

If we know the specific heat of a material, can we determine how much heat is released under a given set of circumstances?
::如果我们知道一种物质的具体热量,我们能否确定在特定情况下释放多少热量?

Section outline

General

特定热量计算

Does water have a high capacity for absorbing heat? ::水是否具有高吸收热量的能力?

Specific Heat Calculations ::特定热量计算

Sample Problem: Calculating Specific Heat ::样本问题:计算特定热量

Summary ::摘要

Review ::回顾

Does water have a high capacity for absorbing heat?
::水是否具有高吸收热量的能力?

Specific Heat Calculations
::特定热量计算

Sample Problem: Calculating Specific Heat
::样本问题:计算特定热量

Summary
::摘要

Review
::回顾