Question

Two solid blocks are in thermal contact with each other, and block A (at 400 K) is hotter than block B (at 300 K). They are insulated around the outside, so no heat can transfer to or from the surroundings. The blocks do not change volume, so no work is done. Both blocks have a mass of 100, .but the specific heat capacity of block A is 2.00J/(g\cdotpK) and the specific heat capacity of block B is 1.00J/(g\cdoptK).

1. If the two blocks reach thermal equilibrium, what will be the final temperature of the system?
A) 350 K
B) 375 K
C) 400 K
D) 325 K
2. How much heat is transferred from block A to block B during the thermal equilibration process?
A) 50J
B) 100J
C) 200J
D) 150J

Answer 1

The final temperature at thermal equilibrium for both blocks is 350 K, corresponding to option A. Block A transfers 50000 J of heat to Block B during thermal equilibration, corresponding to option C.

Step-by-step explanation:

We need to find the final temperature at thermal equilibrium for both blocks and the amount of heat transfer that occurs between them. Block A has a higher initial temperature (400 K) and a specific heat capacity of 2.00 J/(g·K), while Block B has a lower initial temperature (300 K) and a specific heat capacity of 1.00 J/(g·K). Since no heat is lost to the surroundings and the masses of the blocks are the same, we can use the principle of conservation of energy.

Let T be the final temperature. The heat lost by Block A is equal to the heat gained by Block B.

For Block A: Q = m*c*(T_initial - T_final) → Q = 100 g * 2.00 J/(g·K) * (400 K - T) → Q = 20000 J - 200J/K * T

For Block B: Q = m*c*(T_final - T_initial) → Q = 100 g * 1.00 J/(g·K) * (T - 300 K) → Q = 100J/K * T - 30000 J

Equate the heat loss and gain: 20000 J - 200J/K * T = 100J/K * T - 30000 J. Solve for T, which gives T = 350 K, corresponding to option A).

To find the heat transfer, use the expression for Block A or Block B and plug in T = 350 K:

For Block A: Q = 20000 J - 200 J/K * 350 K → Q = 20000 J - 70000 J → Q = -50000 J

The negative sign indicates heat is lost by Block A, so 50000 J is transferred from Block A to Block B, which corresponds to option C).