Physics + Probability Theory

Express C₂ in terms of T₁, T₂, T, and C₁.

Two bodies 1 and 2 with heat capacities C₁ and C₂ and temperatures T₁ and T₂ are brought into thermal contact in a thermostat, after which the temperature T is reached in thermal equilibrium.
Express C₂ in terms of T₁, T₂, T, and C₁.

Solurtion:


Q₁ = C₁ (T-T₁)
Q₂ = C₂ (T-T₂)
Q₁ + Q₂ = 0

C₁ (T-T₁) + C₂(T-T₂)=0
C₂(T-T₂) = C₁ (T₁-T)
C₂ = C₁ (T₁-T) / (T-T₂)

Physics Problem: Two bodies 1 and 2 with heat capacities C₁ and C₂ ...

Two bodies 1 and 2 with heat capacities C₁ and C₂ and temperatures T₁ and T₂ are brought into thermal contact in a thermostat, after which the temperature T is reached in thermal equilibrium. Express T in terms of C₁, C₂, T₁, T₂. 

Problems in Physics: "Two point masses A and B ..."

Problems in Physics.

1. Two point masses A and B are located on the x-axis. When mass A occupies the X_A coordinate and mass B occupies the X_B coordinate, then their common center of gravity is at the X coordinate. Where is their common center of gravity when the first mass occupies the X_A2 coordinate and the second mass occupies the X_B2 coordinate?
2. When two bodies A and B with temperatures T_A and T_B are brought into thermal contact in a thermostat, then temperature T is reached in thermal equilibrium. What temperature will be in thermal equilibrium if the bodies are initially heated to temperatures T_A2 and T_B2?
3. There is a mark on a thin rubber cord somewhere between the ends of the cord. The locations in space of the ends A and B of the stretched cord and the marks on it are given by the vectors: R_A , R_B and R. Express the location of the mark on the cord when the ends of the stretched cord are located at the points given by the vectors R_A2 and R_B2.