At 300 K, for the reaction A → P, the ∆Ssys is 5 J K-1 mol-1. What is the heat absorbed (in kJ mol-1) by the system?
Step 1: Using the relation between heat and entropy
- From thermodynamics, \[ q = T \Delta S_{sys} \] where \( q \) is heat absorbed, \( T \) is temperature, and \( \Delta S \) is entropy change.
Step 2: Substituting values \[ q = (300 K) \times (5 J K^{-1} mol^{-1}) \] \[ = 1500 J mol^{-1} \] \[ = 1.5 \text{ kJ mol}^{-1} \]
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.