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What is the expression for the rate of change of internal energy with respect to temperature at constant volume for an ideal gas, denoted as (du/dv)t?
The expression for the rate of change of internal energy with respect to temperature at constant volume for an ideal gas is denoted as (du/dv)t.
How is the Joule-Thomson effect calculated in thermodynamics?
The Joule-Thomson effect is calculated in thermodynamics by using the Joule-Thomson coefficient, which is the rate of change of temperature with pressure at constant enthalpy. This coefficient is determined by taking the partial derivative of temperature with respect to pressure at constant enthalpy. The formula for the Joule-Thomson coefficient is given by (T/P)H, where is the Joule-Thomson coefficient, T is temperature, P is pressure, and H is enthalpy.
In the ideal gas law PV nRT what happens quantitatively to T if n is halved when P and V are held constant?
If n is halved while P and V are held constant in the ideal gas law, the temperature (T) must also be halved in order to maintain the equality. This is because the product of n and T must remain constant according to the ideal gas law formula.
When the volume is held constant the relationship between pressure and temperature is?
When volume is held constant, the relationship between pressure and temperature is directly proportional. This is known as Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its temperature when volume is constant. This means that as temperature increases, pressure also increases, and vice versa.
What is the significance of the constant "t" in the equation?
The constant "t" in an equation represents time, and its significance lies in determining how the variables in the equation change over time.
What is the derivative of t?
If it is with respect to t: 1 If it is with respect to some other variable (x for example): (dt)/(dx), which is literally read "the derivative of t with respect to x"
What is derivative of 9et?
Assume that the expression is: y = 9e^(t) Remember that the derivative of e^(t) with respect to t is e^(t). If we take the derivative of the function y, we have.. dy/dt = 9 d[e^(t)]/dt = 9e^(t) Note that I factor out the constant 9. If we keep the 9 in the brackets, then the solution doesn't make a difference.
Derivative of x to the power -t?
well if you're finding the derivative with respect to x, it would be -tx^(-t-1)
Is it truethat a particle with a position that is given by and 119909 and 119862 and 1199052 (C is a properly dimensioned constant) has an acceleration given by 4C.?
No, the acceleration of a particle is determined by the second derivative of its position function with respect to time. If the position function is given by x(t) = 119909 + 119862t + 1199052t^2, then the acceleration a(t) would be the derivative of this function with respect to time twice, not just a constant 4C.
Prove that if vector A has constant magnitude then its derivative is perpendicular to vector A?
Suppose A is a vector with real components. A can be written as <f(t), g(t), h(t)>. Since the magnitude of A is constant we have f(t)*f(t) + g(t)*g(t) + h(t)*h(t) = c, where c is a non-negative real number. Take derivative of both sides of equation we get 2*f(t)*df(t)/dt + 2*g(t)*dg(t)/dt + 2*h(t)*dh(t)/dt = 0. Divide both sides by 2, we get f(t)*df(t)/dt + g(t)*dg(t)/dt + h(t)*dh(t)/dt = 0. Thus the dot product of A and its derivative is 0. This implies the angle between A and its derivative is Pi/2. Hence they are perpendicular.
What is the value for acceleration in the x direction?
If x is a function of time, t, then the second derivative of x, with respect to t, is the acceleration in the x direction.
What is the derivative of work and how is it calculated in the context of physics?
In physics, the derivative of work is called power. Power is calculated by taking the derivative of work with respect to time. It represents the rate at which work is done or energy is transferred. Mathematically, power (P) is calculated as the derivative of work (W) with respect to time (t), expressed as P dW/dt.
Instantaneous velocity formula?
v = dx/dt (the derivative of 'x' with respect to 't') where 'x' is the displacement of the objectin a given direction, and 't' is time.
What is acceleration of a particle if position of a particle at any instant of time t is given by x equals t 3?
velocity is 1st derivative of distance with respect to time acceleration is 2nd derivative of distance with respect to time dx/dt = velocity = 3t^2 dv/dt = acceleration = 6t
What is the formula for instantaneous acceleration?
The formula for instantaneous acceleration is given by the derivative of velocity with respect to time: a(t) = dv(t) / dt, where a(t) is the acceleration at time t and v(t) is the velocity at time t.
What is intantaeous speed?
If a body is moving at a non-constant speed then its instantaneous speed is the derivative of its displacement with respect to time.If the body is at positions x(t) and x(t+dt) at times t and t+dt then the instantaneous speed at time t is the limit, as dt tends to 0, of [x(t+dt) - x(t)]/t.In graph terms, it is the gradient of tangent to the displacement-time graph.
What are the relationships between position velocity acceleration and time?
Position is the location of an object at a specific time, velocity is the rate of change of position with respect to time, and acceleration is the rate of change of velocity with respect to time. These quantities are related through calculus: velocity is the derivative of position with respect to time, and acceleration is the derivative of velocity with respect to time.
