TECHNOLOGY 썸네일형 리스트형 Molar Specific Heat of an Ideal Gas For gases, even with the same amount of heat applied, the temperature increase varies depending on how much the volume changes. Thus, to calculate the molar specific heat, one variable must be held constant. Here, we will examine how to determine the molar specific heat at constant volume and at constant pressure for an ideal gas.Molar Specific Heat at Constant VolumeIf we define \(C_V\) as the .. 더보기 Properties of Definite Integrals I have summarized the properties of definite integrals.Reverse Interval$$\int_{a}^{b} f(x) dx = -\int_{b}^{a} f(x) dx$$Addition & Subtraction$$\int_{a}^{b} (f(x) ± g(x)) dx = \int_{a}^{b} f(x) dx ± \int_{a}^{b} g(x) dx$$Multiplication by a Constant$$\int_{a}^{b} cf(x) dx = c\int_{a}^{b} f(x) dx$$Interval Addition$$\int_{a}^{b} f(x) dx = \int_{a}^{c} f(x) dx + \int_{c}^{b} f(x) dx$$ 더보기 Types of Differentiation I have classified differentiation into different types.Classification by OperationMultiplication by a Constant$$(cf(x))'=cf'(x)$$Addition$$(f(x)+g(x))'=f'(x)+g'(x)$$Subtraction$$(f(x)-g(x))'=f'(x)-g'(x)$$Multiplication$$(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)$$Division$$(\frac{g(x)}{f(x)})'=\frac{f(x)g'(x)-f'(x)g(x)}{(f(x))^2}$$Composition (Chain Rule)$$(f(g(x)))'=f'(g(x))·g'(x)$$You can compute \(f'(g(.. 더보기 Finding the Cross Product of 3D Vectors Calculating It through the Magnitudes and the Angle between the Two VectorsThe process is as follows.Let's suppose there are two vectors, \(\overrightarrow{a}\) and \(\overrightarrow{b}\).Let the magnitudes be \(a\) and \(b\), respectively.Let \(\theta\) be the angle between the two vectors.Let the unit vector which is perpendicular to the two vectors be \(\overrightarrow{c}\),If so,$$\overright.. 더보기 Finding the Dot Product of Vectors IntroductionIf the two vectors are as follows$$\overrightarrow{a} = (a_1, a_2, a_3, \cdots), \overrightarrow{b} = (b_1, b_2, b_3, \cdots)$$and \(\theta\) is the angle between the two vectors$$\overrightarrow{a} \cdot \overrightarrow{b} = a_1 b_1 + a_2 b_2 + a_3 b_3 + \cdots$$$$\overrightarrow{a} \cdot \overrightarrow{b} = |\overrightarrow{a}||\overrightarrow{b}|\cos\theta$$ProofThen, let me demo.. 더보기 이전 1 다음