Given below are two statements:
Statement I: Viscosity of liquid decreases with an increase in temperature.
Statement II: The units of viscosity are kg m-1 s-2.
- Viscosity of liquids decreases with increasing temperature.
Step 1: Understanding viscosity behavior
- Viscosity is a measure of a fluid’s resistance to flow.
- As temperature increases, the intermolecular forces weaken, decreasing viscosity.
- This applies to liquids, whereas for gases, viscosity increases with temperature due to molecular kinetic energy increase.
Step 2: Understanding viscosity units
- The SI unit of viscosity is the Pascal-second (Pa·s), which is equivalent to N·s/m2
- This can be written as: Pa·s = kg/m·s
- The given unit (kg m-1 s-2) is incorrect for viscosity but correct for pressure.
Given the function:
\[ f(x) = \begin{cases} \frac{(2x^2 - ax +1) - (ax^2 + 3bx + 2)}{x+1}, & \text{if } x \neq -1 \\ k, & \text{if } x = -1 \end{cases} \]
If \( a, b, k \in \mathbb{R} \) and \( f(x) \) is continuous for all \( x \), then the value of \( k \) is:
Given the function:
\[ f(x) = \begin{cases} \frac{2x e^{1/2x} - 3x e^{-1/2x}}{e^{1/2x} + 4e^{-1/2x}}, & \text{if } x \neq 0 \\ 0, & \text{if } x = 0 \end{cases} \]
Determine the differentiability of \( f(x) \) at \( x = 0 \).
A magnet suspended in a uniform magnetic field is heated so as to reduce its magnetic moment by 19%. By doing this, the time period of the magnet approximately
A Carnot heat engine has an efficiency of 10%. If the same engine is worked backward to obtain a refrigerator, then the coefficient of performance of the refrigerator is
Match the following physical quantities with their respective dimensional formulas.