MCAT Chem/Phys — Hard Concepts: Advanced Applications

Front

Compare the **flow rate** in the aorta vs. capillaries given the continuity equation.

Back

**Flow rate ($Q$) is constant** throughout the circulatory system (assuming steady state, no fluid loss): $Q = A_1v_1 = A_2v_2$. While the total flow rate is the same, **velocity ($v$)** differs drastically. The total cross-sectional area of capillaries is much larger (~1000x) than the aorta, so velocity in capillaries is very slow to allow time for diffusion.

Front

Calculate the **Effective Focal Length** of two thin lenses in contact.

Back

For lenses in contact, powers add: $P_{total} = P_1 + P_2$. Since Power ($P$) is $1/f$ (in meters), the combined focal length $f_{eq}$ is derived as $1/f_{eq} = 1/f_1 + 1/f_2$. Therefore, $f_{eq} = (f_1 \cdot f_2) / (f_1 + f_2)$. This is crucial for microscope and eyepiece combinations.

Front

Determine the **net magnetic force** on a current-carrying loop in a uniform magnetic field.

Back

The net magnetic force on a closed loop in a **uniform** magnetic field is **zero**. While opposite sides of the loop experience forces in opposite directions ($F = ILB \sin \theta$), they cancel out. However, the **net torque** is generally non-zero, given by $\tau = NIAB \sin \theta$, causing rotation.

Front

Apply the **Nernst Equation** at physiological temperature (37°C) for a monovalent ion.

Back

The Nernst equation calculates equilibrium potential: $E = (RT/zF) \ln([Ion]_{out}/[Ion]_{in})$. At 37°C (310K), substituting constants ($R$, $F$) and converting to log base 10 yields the simplified clinical form: $E = (61.5 \text{ mV} / z) \cdot \log_{10}([Ion]_{out}/[Ion]_{in})$. For $Na^+$ ($z=+1$), this dictates the resting potential drive.

Front

Distinguish between **Short-range (Pauli) Repulsion** and **London Dispersion Forces** in molecular stability.

Back

**Pauli Repulsion** is quantum mechanical: electron clouds overlap when atoms are too close, creating a massive potential energy spike that prevents matter from collapsing. **London Dispersion Forces** are attractive: they arise from instantaneous dipole-induced dipoles due to electron correlation. The equilibrium bond distance is where attractive LDFs balance repulsive Pauli forces.